Algebra Examples

$(2 x - 5) (x + 4) = 2 x^{2} + 5 (x + 2)$

Step 1

Simplify $(2 x - 5) (x + 4)$ .

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Step 1.1

Rewrite.

$0 + 0 + (2 x - 5) (x + 4) = 2 x^{2} + 5 (x + 2)$

Step 1.2

Simplify by adding zeros.

$(2 x - 5) (x + 4) = 2 x^{2} + 5 (x + 2)$

Step 1.3

Expand $(2 x - 5) (x + 4)$ using the FOIL Method.

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Step 1.3.1

Apply the distributive property.

$2 x (x + 4) - 5 (x + 4) = 2 x^{2} + 5 (x + 2)$

Step 1.3.2

Apply the distributive property.

$2 x \cdot x + 2 x \cdot 4 - 5 (x + 4) = 2 x^{2} + 5 (x + 2)$

Step 1.3.3

Apply the distributive property.

$2 x \cdot x + 2 x \cdot 4 - 5 x - 5 \cdot 4 = 2 x^{2} + 5 (x + 2)$

Step 1.4

Simplify and combine like terms.

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Step 1.4.1

Simplify each term.

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Step 1.4.1.1

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

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Step 1.4.1.1.1

Move $x$ .

$2 (x \cdot x) + 2 x \cdot 4 - 5 x - 5 \cdot 4 = 2 x^{2} + 5 (x + 2)$

Step 1.4.1.1.2

Multiply $x$ by $x$ .

$2 x^{2} + 2 x \cdot 4 - 5 x - 5 \cdot 4 = 2 x^{2} + 5 (x + 2)$

Step 1.4.1.2

Multiply $4$ by $2$ .

$2 x^{2} + 8 x - 5 x - 5 \cdot 4 = 2 x^{2} + 5 (x + 2)$

Step 1.4.1.3

Multiply $- 5$ by $4$ .

$2 x^{2} + 8 x - 5 x - 20 = 2 x^{2} + 5 (x + 2)$

Step 1.4.2

Subtract $5 x$ from $8 x$ .

$2 x^{2} + 3 x - 20 = 2 x^{2} + 5 (x + 2)$

Step 2

Simplify each term.

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Step 2.1

Apply the distributive property.

$2 x^{2} + 3 x - 20 = 2 x^{2} + 5 x + 5 \cdot 2$

Step 2.2

Multiply $5$ by $2$ .

$2 x^{2} + 3 x - 20 = 2 x^{2} + 5 x + 10$

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.

$2 x^{2} + 3 x - 20 - 2 x^{2} = 5 x + 10$

Step 3.2

Subtract $5 x$ from both sides of the equation.

$2 x^{2} + 3 x - 20 - 2 x^{2} - 5 x = 10$

Step 3.3

Combine the opposite terms in $2 x^{2} + 3 x - 20 - 2 x^{2} - 5 x$ .

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Step 3.3.1

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

$3 x - 20 + 0 - 5 x = 10$

Step 3.3.2

Add $3 x - 20$ and $0$ .

$3 x - 20 - 5 x = 10$

Step 3.4

Subtract $5 x$ from $3 x$ .

$- 2 x - 20 = 10$

Step 4

Move all terms not containing $x$ to the right side of the equation.

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Step 4.1

Add $20$ to both sides of the equation.

$- 2 x = 10 + 20$

Step 4.2

Add $10$ and $20$ .

$- 2 x = 30$

Step 5

Divide each term in $- 2 x = 30$ by $- 2$ and simplify.

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Step 5.1

Divide each term in $- 2 x = 30$ by $- 2$ .

$\frac{- 2 x}{- 2} = \frac{30}{- 2}$

Step 5.2

Simplify the left side.

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Step 5.2.1

Cancel the common factor of $- 2$ .

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Step 5.2.1.1

Cancel the common factor.

$\frac{- 2 x}{- 2} = \frac{30}{- 2}$

Step 5.2.1.2

Divide $x$ by $1$ .

$x = \frac{30}{- 2}$

Step 5.3

Simplify the right side.

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Step 5.3.1

Divide $30$ by $- 2$ .

$x = - 15$