Algebra Examples

$2 x (x - 8) = (x + 1) (2 x - 3)$

Step 1

Simplify $2 x (x - 8)$ .

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Step 1.1

Rewrite.

$0 + 0 + 2 x (x - 8) = (x + 1) (2 x - 3)$

Step 1.2

Simplify by adding zeros.

$2 x (x - 8) = (x + 1) (2 x - 3)$

Step 1.3

Apply the distributive property.

$2 x \cdot x + 2 x \cdot - 8 = (x + 1) (2 x - 3)$

Step 1.4

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

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Step 1.4.1

Move $x$ .

$2 (x \cdot x) + 2 x \cdot - 8 = (x + 1) (2 x - 3)$

Step 1.4.2

Multiply $x$ by $x$ .

$2 x^{2} + 2 x \cdot - 8 = (x + 1) (2 x - 3)$

Step 1.5

Multiply $- 8$ by $2$ .

$2 x^{2} - 16 x = (x + 1) (2 x - 3)$

Step 2

Simplify $(x + 1) (2 x - 3)$ .

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Step 2.1

Expand $(x + 1) (2 x - 3)$ using the FOIL Method.

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Step 2.1.1

Apply the distributive property.

$2 x^{2} - 16 x = x (2 x - 3) + 1 (2 x - 3)$

Step 2.1.2

Apply the distributive property.

$2 x^{2} - 16 x = x (2 x) + x \cdot - 3 + 1 (2 x - 3)$

Step 2.1.3

Apply the distributive property.

$2 x^{2} - 16 x = x (2 x) + x \cdot - 3 + 1 (2 x) + 1 \cdot - 3$

Step 2.2

Simplify and combine like terms.

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Step 2.2.1

Simplify each term.

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Step 2.2.1.1

Rewrite using the commutative property of multiplication.

$2 x^{2} - 16 x = 2 x \cdot x + x \cdot - 3 + 1 (2 x) + 1 \cdot - 3$

Step 2.2.1.2

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

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Step 2.2.1.2.1

Move $x$ .

$2 x^{2} - 16 x = 2 (x \cdot x) + x \cdot - 3 + 1 (2 x) + 1 \cdot - 3$

Step 2.2.1.2.2

Multiply $x$ by $x$ .

$2 x^{2} - 16 x = 2 x^{2} + x \cdot - 3 + 1 (2 x) + 1 \cdot - 3$

Step 2.2.1.3

Move $- 3$ to the left of $x$ .

$2 x^{2} - 16 x = 2 x^{2} - 3 \cdot x + 1 (2 x) + 1 \cdot - 3$

Step 2.2.1.4

Multiply $2 x$ by $1$ .

$2 x^{2} - 16 x = 2 x^{2} - 3 x + 2 x + 1 \cdot - 3$

Step 2.2.1.5

Multiply $- 3$ by $1$ .

$2 x^{2} - 16 x = 2 x^{2} - 3 x + 2 x - 3$

Step 2.2.2

Add $- 3 x$ and $2 x$ .

$2 x^{2} - 16 x = 2 x^{2} - x - 3$

Step 3

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

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Step 3.1

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

$2 x^{2} - 16 x - 2 x^{2} = - x - 3$

Step 3.2

Add $x$ to both sides of the equation.

$2 x^{2} - 16 x - 2 x^{2} + x = - 3$

Step 3.3

Combine the opposite terms in $2 x^{2} - 16 x - 2 x^{2} + x$ .

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Step 3.3.1

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

$- 16 x + 0 + x = - 3$

Step 3.3.2

Add $- 16 x$ and $0$ .

$- 16 x + x = - 3$

Step 3.4

Add $- 16 x$ and $x$ .

$- 15 x = - 3$

Step 4

Divide each term in $- 15 x = - 3$ by $- 15$ and simplify.

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Step 4.1

Divide each term in $- 15 x = - 3$ by $- 15$ .

$\frac{- 15 x}{- 15} = \frac{- 3}{- 15}$

Step 4.2

Simplify the left side.

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Step 4.2.1

Cancel the common factor of $- 15$ .

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Step 4.2.1.1

Cancel the common factor.

$\frac{- 15 x}{- 15} = \frac{- 3}{- 15}$

Step 4.2.1.2

Divide $x$ by $1$ .

$x = \frac{- 3}{- 15}$

Step 4.3

Simplify the right side.

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Step 4.3.1

Cancel the common factor of $- 3$ and $- 15$ .

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Step 4.3.1.1

Factor $- 3$ out of $- 3$ .

$x = \frac{- 3 (1)}{- 15}$

Step 4.3.1.2

Cancel the common factors.

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Step 4.3.1.2.1

Factor $- 3$ out of $- 15$ .

$x = \frac{- 3 \cdot 1}{- 3 \cdot 5}$

Step 4.3.1.2.2

Cancel the common factor.

$x = \frac{- 3 \cdot 1}{- 3 \cdot 5}$

Step 4.3.1.2.3

Rewrite the expression.

$x = \frac{1}{5}$

Step 5