Algebra Examples

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

Step 1

Move all terms to the left side of the equation and simplify.

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Step 1.1

Simplify the left side.

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Step 1.1.1

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

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Step 1.1.1.1

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

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Step 1.1.1.1.1

Apply the distributive property.

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

Step 1.1.1.1.2

Apply the distributive property.

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

Step 1.1.1.1.3

Apply the distributive property.

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

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

Step 1.1.1.2

Simplify and combine like terms.

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Step 1.1.1.2.1

Simplify each term.

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Step 1.1.1.2.1.1

Multiply $x$ by $x$ .

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

Step 1.1.1.2.1.2

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

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

Step 1.1.1.2.1.3

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

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

Step 1.1.1.2.1.4

Multiply $- 1$ by $2$ .

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

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

Step 1.1.1.2.2

Subtract $x$ from $2 x$ .

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

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

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

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

Step 1.2

Simplify the right side.

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Step 1.2.1

Simplify $x (x + 5)$ .

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Step 1.2.1.1

Apply the distributive property.

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

Step 1.2.1.2

Simplify the expression.

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Step 1.2.1.2.1

Multiply $x$ by $x$ .

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

Step 1.2.1.2.2

Move $5$ to the left of $x$ .

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

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

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

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

Step 1.3

Move all the expressions to the left side of the equation.

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Step 1.3.1

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

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

Step 1.3.2

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

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

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

Step 1.4

Simplify $x^{2} + x - 2 - x^{2} - 5 x$ .

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Step 1.4.1

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

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Step 1.4.1.1

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

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

Step 1.4.1.2

Add $x - 2$ and $0$ .

$x - 2 - 5 x = 0$

$x - 2 - 5 x = 0$

Step 1.4.2

Subtract $5 x$ from $x$ .

$- 4 x - 2 = 0$

$- 4 x - 2 = 0$

$- 4 x - 2 = 0$

Step 2

Add $2$ to both sides of the equation.

$- 4 x = 2$

Step 3

Divide each term in $- 4 x = 2$ by $- 4$ and simplify.

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Step 3.1

Divide each term in $- 4 x = 2$ by $- 4$ .

$\frac{- 4 x}{- 4} = \frac{2}{- 4}$

Step 3.2

Simplify the left side.

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Step 3.2.1

Cancel the common factor of $- 4$ .

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Step 3.2.1.1

Cancel the common factor.

$\frac{- 4 x}{- 4} = \frac{2}{- 4}$

Step 3.2.1.2

Divide $x$ by $1$ .

$x = \frac{2}{- 4}$

$x = \frac{2}{- 4}$

$x = \frac{2}{- 4}$

Step 3.3

Simplify the right side.

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Step 3.3.1

Cancel the common factor of $2$ and $- 4$ .

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Step 3.3.1.1

Factor $2$ out of $2$ .

$x = \frac{2 (1)}{- 4}$

Step 3.3.1.2

Cancel the common factors.

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Step 3.3.1.2.1

Factor $2$ out of $- 4$ .

$x = \frac{2 \cdot 1}{2 \cdot - 2}$

Step 3.3.1.2.2

Cancel the common factor.

$x = \frac{2 \cdot 1}{2 \cdot - 2}$

Step 3.3.1.2.3

Rewrite the expression.

$x = \frac{1}{- 2}$

$x = \frac{1}{- 2}$

$x = \frac{1}{- 2}$

Step 3.3.2

Move the negative in front of the fraction.

$x = - \frac{1}{2}$

$x = - \frac{1}{2}$

$x = - \frac{1}{2}$

$[\begin{array}{c} x^{2} & \frac{1}{2} \\ \sqrt{π} & \int x d x \end{array}]$