Solve for x -3x(16x^2-25)(x^2-13)=0

$- 3 x (16 x^{2} - 25) (x^{2} - 13) = 0$

Step 1

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

$x = 0$

$16 x^{2} - 25 = 0$

$x^{2} - 13 = 0$

Step 2

Set $x$ equal to $0$ .

$x = 0$

Step 3

Set $16 x^{2} - 25$ equal to $0$ and solve for $x$ .

Set $16 x^{2} - 25$ equal to $0$ .

$16 x^{2} - 25 = 0$

Solve $16 x^{2} - 25 = 0$ for $x$ .

Add $25$ to both sides of the equation.

$16 x^{2} = 25$

Divide each term in $16 x^{2} = 25$ by $16$ and simplify.

Divide each term in $16 x^{2} = 25$ by $16$ .

$\frac{16 x^{2}}{16} = \frac{25}{16}$

Simplify the left side.

Cancel the common factor of $16$ .

Cancel the common factor.

$\frac{16 x^{2}}{16} = \frac{25}{16}$

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

$x^{2} = \frac{25}{16}$

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

$x = \pm \sqrt{\frac{25}{16}}$

Simplify $\pm \sqrt{\frac{25}{16}}$ .

Rewrite $\sqrt{\frac{25}{16}}$ as $\frac{\sqrt{25}}{\sqrt{16}}$ .

$x = \pm \frac{\sqrt{25}}{\sqrt{16}}$

Simplify the numerator.

Rewrite $25$ as $5^{2}$ .

$x = \pm \frac{\sqrt{5^{2}}}{\sqrt{16}}$

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

$x = \pm \frac{5}{\sqrt{16}}$

Simplify the denominator.

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

$x = \pm \frac{5}{\sqrt{4^{2}}}$

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

$x = \pm \frac{5}{4}$

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.

$x = \frac{5}{4}$

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

$x = - \frac{5}{4}$

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

$x = \frac{5}{4}, - \frac{5}{4}$

Step 4

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 5

The final solution is all the values that make $- 3 x (16 x^{2} - 25) (x^{2} - 13) = 0$ true.

$x = 0, \frac{5}{4}, - \frac{5}{4}, \sqrt{13}, - \sqrt{13}$

Step 6

The result can be shown in multiple forms.

Exact Form:

$x = 0, \frac{5}{4}, - \frac{5}{4}, \sqrt{13}, - \sqrt{13}$

Decimal Form:

$x = 0, 1.25, - 1.25, 3.60555127 \dots, - 3.60555127 \dots$

Mixed Number Form:

$x = 0, 1 \frac{1}{4}, - 1 \frac{1}{4}, \sqrt{13}, - \sqrt{13}$

Solve for x -3x(16x^2-25)(x^2-13)=0

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