Solve for x 2x(x-3)(64x^2-25)=0

$2 x (x - 3) (64 x^{2} - 25) = 0$

Step 1

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

$x = 0$

$x - 3 = 0$

$64 x^{2} - 25 = 0$

Step 2

Set $x$ equal to $0$ .

$x = 0$

Step 3

Set $x - 3$ equal to $0$ and solve for $x$ .

Set $x - 3$ equal to $0$ .

$x - 3 = 0$

Add $3$ to both sides of the equation.

$x = 3$

Step 4

Set $64 x^{2} - 25$ equal to $0$ and solve for $x$ .

Set $64 x^{2} - 25$ equal to $0$ .

$64 x^{2} - 25 = 0$

Solve $64 x^{2} - 25 = 0$ for $x$ .

Add $25$ to both sides of the equation.

$64 x^{2} = 25$

Divide each term in $64 x^{2} = 25$ by $64$ and simplify.

Divide each term in $64 x^{2} = 25$ by $64$ .

$\frac{64 x^{2}}{64} = \frac{25}{64}$

Simplify the left side.

Cancel the common factor of $64$ .

Cancel the common factor.

$\frac{64 x^{2}}{64} = \frac{25}{64}$

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

$x^{2} = \frac{25}{64}$

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

$x = \pm \sqrt{\frac{25}{64}}$

Simplify $\pm \sqrt{\frac{25}{64}}$ .

Rewrite $\sqrt{\frac{25}{64}}$ as $\frac{\sqrt{25}}{\sqrt{64}}$ .

$x = \pm \frac{\sqrt{25}}{\sqrt{64}}$

Simplify the numerator.

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

$x = \pm \frac{\sqrt{5^{2}}}{\sqrt{64}}$

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

$x = \pm \frac{5}{\sqrt{64}}$

Simplify the denominator.

Rewrite $64$ as $8^{2}$ .

$x = \pm \frac{5}{\sqrt{8^{2}}}$

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

$x = \pm \frac{5}{8}$

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.

$x = \frac{5}{8}$

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

$x = - \frac{5}{8}$

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

$x = \frac{5}{8}, - \frac{5}{8}$

Step 5

The final solution is all the values that make $2 x (x - 3) (64 x^{2} - 25) = 0$ true.

$x = 0, 3, \frac{5}{8}, - \frac{5}{8}$

Step 6

The result can be shown in multiple forms.

Exact Form:

$x = 0, 3, \frac{5}{8}, - \frac{5}{8}$

Decimal Form:

$x = 0, 3, 0.625, - 0.625$

Solve for x 2x(x-3)(64x^2-25)=0

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