Algebra Examples

$x - 3 x (1 - 12 x) = 11 - (5 - 6 x) (6 x + 5)$

Step 1

Simplify $x - 3 x (1 - 12 x)$ .

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Step 1.1

Simplify each term.

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Step 1.1.1

Apply the distributive property.

$x - 3 x \cdot 1 - 3 x (- 12 x) = 11 - (5 - 6 x) (6 x + 5)$

Step 1.1.2

Multiply $- 3$ by $1$ .

$x - 3 x - 3 x (- 12 x) = 11 - (5 - 6 x) (6 x + 5)$

Step 1.1.3

Rewrite using the commutative property of multiplication.

$x - 3 x - 3 \cdot - 12 x \cdot x = 11 - (5 - 6 x) (6 x + 5)$

Step 1.1.4

Simplify each term.

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Step 1.1.4.1

Multiply $x$ by $x$ by adding the exponents.

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Step 1.1.4.1.1

Move $x$ .

$x - 3 x - 3 \cdot - 12 (x \cdot x) = 11 - (5 - 6 x) (6 x + 5)$

Step 1.1.4.1.2

Multiply $x$ by $x$ .

$x - 3 x - 3 \cdot - 12 x^{2} = 11 - (5 - 6 x) (6 x + 5)$

Step 1.1.4.2

Multiply $- 3$ by $- 12$ .

$x - 3 x + 36 x^{2} = 11 - (5 - 6 x) (6 x + 5)$

Step 1.2

Subtract $3 x$ from $x$ .

$- 2 x + 36 x^{2} = 11 - (5 - 6 x) (6 x + 5)$

Step 2

Simplify $11 - (5 - 6 x) (6 x + 5)$ .

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Step 2.1

Simplify each term.

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Step 2.1.1

Apply the distributive property.

$- 2 x + 36 x^{2} = 11 + (- 1 \cdot 5 - (- 6 x)) (6 x + 5)$

Step 2.1.2

Multiply $- 1$ by $5$ .

$- 2 x + 36 x^{2} = 11 + (- 5 - (- 6 x)) (6 x + 5)$

Step 2.1.3

Multiply $- 6$ by $- 1$ .

$- 2 x + 36 x^{2} = 11 + (- 5 + 6 x) (6 x + 5)$

Step 2.1.4

Expand $(- 5 + 6 x) (6 x + 5)$ using the FOIL Method.

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Step 2.1.4.1

Apply the distributive property.

$- 2 x + 36 x^{2} = 11 - 5 (6 x + 5) + 6 x (6 x + 5)$

Step 2.1.4.2

Apply the distributive property.

$- 2 x + 36 x^{2} = 11 - 5 (6 x) - 5 \cdot 5 + 6 x (6 x + 5)$

Step 2.1.4.3

Apply the distributive property.

$- 2 x + 36 x^{2} = 11 - 5 (6 x) - 5 \cdot 5 + 6 x (6 x) + 6 x \cdot 5$

Step 2.1.5

Combine the opposite terms in $- 5 (6 x) - 5 \cdot 5 + 6 x (6 x) + 6 x \cdot 5$ .

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Step 2.1.5.1

Reorder the factors in the terms $- 5 (6 x)$ and $6 x \cdot 5$ .

$- 2 x + 36 x^{2} = 11 - 5 \cdot 6 x - 5 \cdot 5 + 6 x (6 x) + 5 \cdot 6 x$

Step 2.1.5.2

Add $- 5 \cdot 6 x$ and $5 \cdot 6 x$ .

$- 2 x + 36 x^{2} = 11 + 0 - 5 \cdot 5 + 6 x (6 x)$

Step 2.1.5.3

Subtract $5 \cdot 5$ from $0$ .

$- 2 x + 36 x^{2} = 11 - 5 \cdot 5 + 6 x (6 x)$

Step 2.1.6

Simplify each term.

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Step 2.1.6.1

Multiply $- 5$ by $5$ .

$- 2 x + 36 x^{2} = 11 - 25 + 6 x (6 x)$

Step 2.1.6.2

Rewrite using the commutative property of multiplication.

$- 2 x + 36 x^{2} = 11 - 25 + 6 \cdot 6 x \cdot x$

Step 2.1.6.3

Multiply $x$ by $x$ by adding the exponents.

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Step 2.1.6.3.1

Move $x$ .

$- 2 x + 36 x^{2} = 11 - 25 + 6 \cdot 6 (x \cdot x)$

Step 2.1.6.3.2

Multiply $x$ by $x$ .

$- 2 x + 36 x^{2} = 11 - 25 + 6 \cdot 6 x^{2}$

Step 2.1.6.4

Multiply $6$ by $6$ .

$- 2 x + 36 x^{2} = 11 - 25 + 36 x^{2}$

Step 2.2

Subtract $25$ from $11$ .

$- 2 x + 36 x^{2} = - 14 + 36 x^{2}$

Step 3

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

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Step 3.1

Subtract $36 x^{2}$ from both sides of the equation.

$- 2 x + 36 x^{2} - 36 x^{2} = - 14$

Step 3.2

Combine the opposite terms in $- 2 x + 36 x^{2} - 36 x^{2}$ .

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Step 3.2.1

Subtract $36 x^{2}$ from $36 x^{2}$ .

$- 2 x + 0 = - 14$

Step 3.2.2

Add $- 2 x$ and $0$ .

$- 2 x = - 14$

Step 4

Divide each term in $- 2 x = - 14$ by $- 2$ and simplify.

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Step 4.1

Divide each term in $- 2 x = - 14$ by $- 2$ .

$\frac{- 2 x}{- 2} = \frac{- 14}{- 2}$

Step 4.2

Simplify the left side.

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Step 4.2.1

Cancel the common factor of $- 2$ .

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Step 4.2.1.1

Cancel the common factor.

$\frac{- 2 x}{- 2} = \frac{- 14}{- 2}$

Step 4.2.1.2

Divide $x$ by $1$ .

$x = \frac{- 14}{- 2}$

Step 4.3

Simplify the right side.

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Step 4.3.1

Divide $- 14$ by $- 2$ .

$x = 7$