Solve for x -3x(x^2-14)(x^2+16)=0

$- 3 x (x^{2} - 14) (x^{2} + 16) = 0$

Step 1

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

$x = 0$

$x^{2} - 14 = 0$

$x^{2} + 16 = 0$

Step 2

Set $x$ equal to $0$ .

$x = 0$

Step 3

Set $x^{2} - 14$ equal to $0$ and solve for $x$ .

Set $x^{2} - 14$ equal to $0$ .

$x^{2} - 14 = 0$

Solve $x^{2} - 14 = 0$ for $x$ .

Add $14$ to both sides of the equation.

$x^{2} = 14$

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

$x = \pm \sqrt{14}$

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.

$x = \sqrt{14}$

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

$x = - \sqrt{14}$

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

$x = \sqrt{14}, - \sqrt{14}$

Step 4

Set $x^{2} + 16$ equal to $0$ and solve for $x$ .

Set $x^{2} + 16$ equal to $0$ .

$x^{2} + 16 = 0$

Solve $x^{2} + 16 = 0$ for $x$ .

Subtract $16$ from both sides of the equation.

$x^{2} = - 16$

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

$x = \pm \sqrt{- 16}$

Simplify $\pm \sqrt{- 16}$ .

Rewrite $- 16$ as $- 1 (16)$ .

$x = \pm \sqrt{- 1 (16)}$

Rewrite $\sqrt{- 1 (16)}$ as $\sqrt{- 1} \cdot \sqrt{16}$ .

$x = \pm \sqrt{- 1} \cdot \sqrt{16}$

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

$x = \pm i \cdot \sqrt{16}$

Rewrite $16$ as $4^{2}$ .

$x = \pm i \cdot \sqrt{4^{2}}$

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

$x = \pm i \cdot 4$

Move $4$ to the left of $i$ .

$x = \pm 4 i$

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.

$x = 4 i$

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

$x = - 4 i$

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

$x = 4 i, - 4 i$

Step 5

The final solution is all the values that make $- 3 x (x^{2} - 14) (x^{2} + 16) = 0$ true.

$x = 0, \sqrt{14}, - \sqrt{14}, 4 i, - 4 i$

Solve for x -3x(x^2-14)(x^2+16)=0

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