Solve for x -2(x^2-13)(x^2+9)=0

$- 2 (x^{2} - 13) (x^{2} + 9) = 0$

Step 1

If any individual factor on the left side of the equation is equal to $0$ , the entire expression will be equal to $0$ .

$x^{2} - 13 = 0$

$x^{2} + 9 = 0$

Step 2

Set $x^{2} - 13$ equal to $0$ and solve for $x$ .

Set $x^{2} - 13$ equal to $0$ .

$x^{2} - 13 = 0$

Solve $x^{2} - 13 = 0$ for $x$ .

Add $13$ to both sides of the equation.

$x^{2} = 13$

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

$x = \pm \sqrt{13}$

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

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

$x = \sqrt{13}$

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

$x = - \sqrt{13}$

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

$x = \sqrt{13}, - \sqrt{13}$

Step 3

Set $x^{2} + 9$ equal to $0$ and solve for $x$ .

Set $x^{2} + 9$ equal to $0$ .

$x^{2} + 9 = 0$

Solve $x^{2} + 9 = 0$ for $x$ .

Subtract $9$ from both sides of the equation.

$x^{2} = - 9$

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

$x = \pm \sqrt{- 9}$

Simplify $\pm \sqrt{- 9}$ .

Rewrite $- 9$ as $- 1 (9)$ .

$x = \pm \sqrt{- 1 (9)}$

Rewrite $\sqrt{- 1 (9)}$ as $\sqrt{- 1} \cdot \sqrt{9}$ .

$x = \pm \sqrt{- 1} \cdot \sqrt{9}$

Rewrite $\sqrt{- 1}$ as $i$ .

$x = \pm i \cdot \sqrt{9}$

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

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

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

$x = \pm i \cdot 3$

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

$x = \pm 3 i$

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

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

$x = 3 i$

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

$x = - 3 i$

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

$x = 3 i, - 3 i$

Step 4

The final solution is all the values that make $- 2 (x^{2} - 13) (x^{2} + 9) = 0$ true.

$x = \sqrt{13}, - \sqrt{13}, 3 i, - 3 i$

Solve for x -2(x^2-13)(x^2+9)=0

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