Pre-Algebra Examples

$9 x^{2} + 3 = 4 (3 x^{2} - 6)$

Step 1

Simplify $4 (3 x^{2} - 6)$ .

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Step 1.1

Rewrite.

$9 x^{2} + 3 = 0 + 0 + 4 (3 x^{2} - 6)$

Step 1.2

Simplify by adding zeros.

$9 x^{2} + 3 = 4 (3 x^{2} - 6)$

Step 1.3

Apply the distributive property.

$9 x^{2} + 3 = 4 (3 x^{2}) + 4 \cdot - 6$

Step 1.4

Multiply.

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Step 1.4.1

Multiply $3$ by $4$ .

$9 x^{2} + 3 = 12 x^{2} + 4 \cdot - 6$

Step 1.4.2

Multiply $4$ by $- 6$ .

$9 x^{2} + 3 = 12 x^{2} - 24$

Step 2

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

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Step 2.1

Subtract $12 x^{2}$ from both sides of the equation.

$9 x^{2} + 3 - 12 x^{2} = - 24$

Step 2.2

Subtract $12 x^{2}$ from $9 x^{2}$ .

$- 3 x^{2} + 3 = - 24$

Step 3

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

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Step 3.1

Subtract $3$ from both sides of the equation.

$- 3 x^{2} = - 24 - 3$

Step 3.2

Subtract $3$ from $- 24$ .

$- 3 x^{2} = - 27$

Step 4

Divide each term in $- 3 x^{2} = - 27$ by $- 3$ and simplify.

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Step 4.1

Divide each term in $- 3 x^{2} = - 27$ by $- 3$ .

$\frac{- 3 x^{2}}{- 3} = \frac{- 27}{- 3}$

Step 4.2

Simplify the left side.

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Step 4.2.1

Cancel the common factor of $- 3$ .

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Step 4.2.1.1

Cancel the common factor.

$\frac{- 3 x^{2}}{- 3} = \frac{- 27}{- 3}$

Step 4.2.1.2

Divide $x^{2}$ by $1$ .

$x^{2} = \frac{- 27}{- 3}$

Step 4.3

Simplify the right side.

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Step 4.3.1

Divide $- 27$ by $- 3$ .

$x^{2} = 9$

Step 5

Take the specified root of both sides of the equation to eliminate the exponent on the left side.

$x = \pm \sqrt{9}$

Step 6

Simplify $\pm \sqrt{9}$ .

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Step 6.1

Rewrite $9$ as $3^{2}$ .

$x = \pm \sqrt{3^{2}}$

Step 6.2

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

$x = \pm 3$

Step 7

The complete solution is the result of both the positive and negative portions of the solution.

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Step 7.1

First, use the positive value of the $\pm$ to find the first solution.

$x = 3$

Step 7.2

Next, use the negative value of the $\pm$ to find the second solution.

$x = - 3$

Step 7.3

The complete solution is the result of both the positive and negative portions of the solution.

$x = 3, - 3$