Algebra Examples

$6 x^{3} (2 x + 4) = 2 x (6 x^{3} + 12 x^{2} - 10) + 60$

Step 1

Since $x$ is on the right side of the equation, switch the sides so it is on the left side of the equation.

$2 x (6 x^{3} + 12 x^{2} - 10) + 60 = 6 x^{3} (2 x + 4)$

Step 2

Simplify each term.

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Step 2.1

Apply the distributive property.

$2 x (6 x^{3}) + 2 x (12 x^{2}) + 2 x \cdot - 10 + 60 = 6 x^{3} (2 x + 4)$

Step 2.2

Simplify.

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Step 2.2.1

Rewrite using the commutative property of multiplication.

$2 \cdot 6 x \cdot x^{3} + 2 x (12 x^{2}) + 2 x \cdot - 10 + 60 = 6 x^{3} (2 x + 4)$

Step 2.2.2

Rewrite using the commutative property of multiplication.

$2 \cdot 6 x \cdot x^{3} + 2 \cdot 12 x \cdot x^{2} + 2 x \cdot - 10 + 60 = 6 x^{3} (2 x + 4)$

Step 2.2.3

Multiply $- 10$ by $2$ .

$2 \cdot 6 x \cdot x^{3} + 2 \cdot 12 x \cdot x^{2} - 20 x + 60 = 6 x^{3} (2 x + 4)$

Step 2.3

Simplify each term.

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Step 2.3.1

Multiply $x$ by $x^{3}$ by adding the exponents.

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Step 2.3.1.1

Move $x^{3}$ .

$2 \cdot 6 (x^{3} x) + 2 \cdot 12 x \cdot x^{2} - 20 x + 60 = 6 x^{3} (2 x + 4)$

Step 2.3.1.2

Multiply $x^{3}$ by $x$ .

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Step 2.3.1.2.1

Raise $x$ to the power of $1$ .

$2 \cdot 6 (x^{3} x^{1}) + 2 \cdot 12 x \cdot x^{2} - 20 x + 60 = 6 x^{3} (2 x + 4)$

Step 2.3.1.2.2

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

$2 \cdot 6 x^{3 + 1} + 2 \cdot 12 x \cdot x^{2} - 20 x + 60 = 6 x^{3} (2 x + 4)$

Step 2.3.1.3

Add $3$ and $1$ .

$2 \cdot 6 x^{4} + 2 \cdot 12 x \cdot x^{2} - 20 x + 60 = 6 x^{3} (2 x + 4)$

Step 2.3.2

Multiply $2$ by $6$ .

$12 x^{4} + 2 \cdot 12 x \cdot x^{2} - 20 x + 60 = 6 x^{3} (2 x + 4)$

Step 2.3.3

Multiply $x$ by $x^{2}$ by adding the exponents.

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Step 2.3.3.1

Move $x^{2}$ .

$12 x^{4} + 2 \cdot 12 (x^{2} x) - 20 x + 60 = 6 x^{3} (2 x + 4)$

Step 2.3.3.2

Multiply $x^{2}$ by $x$ .

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Step 2.3.3.2.1

Raise $x$ to the power of $1$ .

$12 x^{4} + 2 \cdot 12 (x^{2} x^{1}) - 20 x + 60 = 6 x^{3} (2 x + 4)$

Step 2.3.3.2.2

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

$12 x^{4} + 2 \cdot 12 x^{2 + 1} - 20 x + 60 = 6 x^{3} (2 x + 4)$

Step 2.3.3.3

Add $2$ and $1$ .

$12 x^{4} + 2 \cdot 12 x^{3} - 20 x + 60 = 6 x^{3} (2 x + 4)$

Step 2.3.4

Multiply $2$ by $12$ .

$12 x^{4} + 24 x^{3} - 20 x + 60 = 6 x^{3} (2 x + 4)$

Step 3

Simplify $6 x^{3} (2 x + 4)$ .

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Step 3.1

Simplify by multiplying through.

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Step 3.1.1

Apply the distributive property.

$12 x^{4} + 24 x^{3} - 20 x + 60 = 6 x^{3} (2 x) + 6 x^{3} \cdot 4$

Step 3.1.2

Simplify the expression.

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Step 3.1.2.1

Rewrite using the commutative property of multiplication.

$12 x^{4} + 24 x^{3} - 20 x + 60 = 6 \cdot 2 x^{3} x + 6 x^{3} \cdot 4$

Step 3.1.2.2

Multiply $4$ by $6$ .

$12 x^{4} + 24 x^{3} - 20 x + 60 = 6 \cdot 2 x^{3} x + 24 x^{3}$

Step 3.2

Simplify each term.

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Step 3.2.1

Multiply $x^{3}$ by $x$ by adding the exponents.

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Step 3.2.1.1

Move $x$ .

$12 x^{4} + 24 x^{3} - 20 x + 60 = 6 \cdot 2 (x \cdot x^{3}) + 24 x^{3}$

Step 3.2.1.2

Multiply $x$ by $x^{3}$ .

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Step 3.2.1.2.1

Raise $x$ to the power of $1$ .

$12 x^{4} + 24 x^{3} - 20 x + 60 = 6 \cdot 2 (x^{1} x^{3}) + 24 x^{3}$

Step 3.2.1.2.2

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

$12 x^{4} + 24 x^{3} - 20 x + 60 = 6 \cdot 2 x^{1 + 3} + 24 x^{3}$

Step 3.2.1.3

Add $1$ and $3$ .

$12 x^{4} + 24 x^{3} - 20 x + 60 = 6 \cdot 2 x^{4} + 24 x^{3}$

Step 3.2.2

Multiply $6$ by $2$ .

$12 x^{4} + 24 x^{3} - 20 x + 60 = 12 x^{4} + 24 x^{3}$

Step 4

Move all terms containing $x$ to the left side of the equation.

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Step 4.1

Subtract $12 x^{4}$ from both sides of the equation.

$12 x^{4} + 24 x^{3} - 20 x + 60 - 12 x^{4} = 24 x^{3}$

Step 4.2

Subtract $24 x^{3}$ from both sides of the equation.

$12 x^{4} + 24 x^{3} - 20 x + 60 - 12 x^{4} - 24 x^{3} = 0$

Step 4.3

Combine the opposite terms in $12 x^{4} + 24 x^{3} - 20 x + 60 - 12 x^{4} - 24 x^{3}$ .

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Step 4.3.1

Subtract $12 x^{4}$ from $12 x^{4}$ .

$24 x^{3} - 20 x + 60 + 0 - 24 x^{3} = 0$

Step 4.3.2

Add $24 x^{3} - 20 x + 60$ and $0$ .

$24 x^{3} - 20 x + 60 - 24 x^{3} = 0$

Step 4.3.3

Subtract $24 x^{3}$ from $24 x^{3}$ .

$- 20 x + 60 + 0 = 0$

Step 4.3.4

Add $- 20 x + 60$ and $0$ .

$- 20 x + 60 = 0$

Step 5

Subtract $60$ from both sides of the equation.

$- 20 x = - 60$

Step 6

Divide each term in $- 20 x = - 60$ by $- 20$ and simplify.

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Step 6.1

Divide each term in $- 20 x = - 60$ by $- 20$ .

$\frac{- 20 x}{- 20} = \frac{- 60}{- 20}$

Step 6.2

Simplify the left side.

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Step 6.2.1

Cancel the common factor of $- 20$ .

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Step 6.2.1.1

Cancel the common factor.

$\frac{- 20 x}{- 20} = \frac{- 60}{- 20}$

Step 6.2.1.2

Divide $x$ by $1$ .

$x = \frac{- 60}{- 20}$

Step 6.3

Simplify the right side.

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Step 6.3.1

Divide $- 60$ by $- 20$ .

$x = 3$