Algebra Examples

$x (x - 6) = 4 (x + 6)$

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 $x (x - 6)$ .

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Step 1.1.1.1

Apply the distributive property.

$x \cdot x + x \cdot - 6 = 4 (x + 6)$

Step 1.1.1.2

Simplify the expression.

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Step 1.1.1.2.1

Multiply $x$ by $x$ .

$x^{2} + x \cdot - 6 = 4 (x + 6)$

Step 1.1.1.2.2

Move $- 6$ to the left of $x$ .

$x^{2} - 6 x = 4 (x + 6)$

Step 1.2

Simplify the right side.

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Step 1.2.1

Simplify $4 (x + 6)$ .

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Step 1.2.1.1

Apply the distributive property.

$x^{2} - 6 x = 4 x + 4 \cdot 6$

Step 1.2.1.2

Multiply $4$ by $6$ .

$x^{2} - 6 x = 4 x + 24$

Step 1.3

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

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Step 1.3.1

Subtract $4 x$ from both sides of the equation.

$x^{2} - 6 x - 4 x = 24$

Step 1.3.2

Subtract $24$ from both sides of the equation.

$x^{2} - 6 x - 4 x - 24 = 0$

Step 1.4

Subtract $4 x$ from $- 6 x$ .

$x^{2} - 10 x - 24 = 0$

Step 2

Use the quadratic formula to find the solutions.

$\frac{- b \pm \sqrt{b^{2} - 4 (a c)}}{2 a}$

Step 3

Substitute the values $a = 1$ , $b = - 10$ , and $c = - 24$ into the quadratic formula and solve for $x$ .

$\frac{10 \pm \sqrt{{(- 10)}^{2} - 4 \cdot (1 \cdot - 24)}}{2 \cdot 1}$

Step 4

Simplify.

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Step 4.1

Simplify the numerator.

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Step 4.1.1

Raise $- 10$ to the power of $2$ .

$x = \frac{10 \pm \sqrt{100 - 4 \cdot 1 \cdot - 24}}{2 \cdot 1}$

Step 4.1.2

Multiply $- 4 \cdot 1 \cdot - 24$ .

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Step 4.1.2.1

Multiply $- 4$ by $1$ .

$x = \frac{10 \pm \sqrt{100 - 4 \cdot - 24}}{2 \cdot 1}$

Step 4.1.2.2

Multiply $- 4$ by $- 24$ .

$x = \frac{10 \pm \sqrt{100 + 96}}{2 \cdot 1}$

Step 4.1.3

Add $100$ and $96$ .

$x = \frac{10 \pm \sqrt{196}}{2 \cdot 1}$

Step 4.1.4

Rewrite $196$ as $14^{2}$ .

$x = \frac{10 \pm \sqrt{14^{2}}}{2 \cdot 1}$

Step 4.1.5

Pull terms out from under the radical, assuming positive real numbers.

$x = \frac{10 \pm 14}{2 \cdot 1}$

Step 4.2

Multiply $2$ by $1$ .

$x = \frac{10 \pm 14}{2}$

Step 4.3

Simplify $\frac{10 \pm 14}{2}$ .

$x = 5 \pm 7$

Step 5

The final answer is the combination of both solutions.

$x = 12, - 2$