Algebra Examples

$(x - 1) (x + 2) = x (x + 5)$

Step 1

Subtract $x (x + 5)$ from both sides of the equation.

$(x - 1) (x + 2) - x (x + 5) = 0$

Step 2

Simplify $(x - 1) (x + 2) - x (x + 5)$ .

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Step 2.1

Simplify each term.

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Step 2.1.1

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

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Step 2.1.1.1

Apply the distributive property.

$x (x + 2) - 1 (x + 2) - x (x + 5) = 0$

Step 2.1.1.2

Apply the distributive property.

$x \cdot x + x \cdot 2 - 1 (x + 2) - x (x + 5) = 0$

Step 2.1.1.3

Apply the distributive property.

$x \cdot x + x \cdot 2 - 1 x - 1 \cdot 2 - x (x + 5) = 0$

Step 2.1.2

Simplify and combine like terms.

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Step 2.1.2.1

Simplify each term.

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Step 2.1.2.1.1

Multiply $x$ by $x$ .

$x^{2} + x \cdot 2 - 1 x - 1 \cdot 2 - x (x + 5) = 0$

Step 2.1.2.1.2

Move $2$ to the left of $x$ .

$x^{2} + 2 \cdot x - 1 x - 1 \cdot 2 - x (x + 5) = 0$

Step 2.1.2.1.3

Rewrite $- 1 x$ as $- x$ .

$x^{2} + 2 x - x - 1 \cdot 2 - x (x + 5) = 0$

Step 2.1.2.1.4

Multiply $- 1$ by $2$ .

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

Step 2.1.2.2

Subtract $x$ from $2 x$ .

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

Step 2.1.3

Apply the distributive property.

$x^{2} + x - 2 - x \cdot x - x \cdot 5 = 0$

Step 2.1.4

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

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Step 2.1.4.1

Move $x$ .

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

Step 2.1.4.2

Multiply $x$ by $x$ .

$x^{2} + x - 2 - x^{2} - x \cdot 5 = 0$

Step 2.1.5

Multiply $5$ by $- 1$ .

$x^{2} + x - 2 - x^{2} - 5 x = 0$

Step 2.2

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

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Step 2.2.1

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

$x - 2 + 0 - 5 x = 0$

Step 2.2.2

Add $x - 2$ and $0$ .

$x - 2 - 5 x = 0$

Step 2.3

Subtract $5 x$ from $x$ .

$- 4 x - 2 = 0$

Step 3