Algebra Examples

$x (x + 3) - 6 = x^{2} + 5 x - 8$

Step 1

Simplify each term.

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Step 1.1

Apply the distributive property.

$x \cdot x + x \cdot 3 - 6 = x^{2} + 5 x - 8$

Step 1.2

Multiply $x$ by $x$ .

$x^{2} + x \cdot 3 - 6 = x^{2} + 5 x - 8$

Step 1.3

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

$x^{2} + 3 x - 6 = x^{2} + 5 x - 8$

Step 2

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

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Step 2.1

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

$x^{2} + 3 x - 6 - x^{2} = 5 x - 8$

Step 2.2

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

$x^{2} + 3 x - 6 - x^{2} - 5 x = - 8$

Step 2.3

Combine the opposite terms in $x^{2} + 3 x - 6 - x^{2} - 5 x$ .

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Step 2.3.1

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

$3 x - 6 + 0 - 5 x = - 8$

Step 2.3.2

Add $3 x - 6$ and $0$ .

$3 x - 6 - 5 x = - 8$

Step 2.4

Subtract $5 x$ from $3 x$ .

$- 2 x - 6 = - 8$

Step 3

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

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Step 3.1

Add $6$ to both sides of the equation.

$- 2 x = - 8 + 6$

Step 3.2

Add $- 8$ and $6$ .

$- 2 x = - 2$

Step 4

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

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Step 4.1

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

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

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.

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

Step 4.2.1.2

Divide $x$ by $1$ .

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

Step 4.3

Simplify the right side.

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Step 4.3.1

Divide $- 2$ by $- 2$ .

$x = 1$