Solve for x 2(2x-3)(100x^2-81)=0

$2 (2 x - 3) (100 x^{2} - 81) = 0$

Step 1

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

$2 x - 3 = 0$

$100 x^{2} - 81 = 0$

Step 2

Set $2 x - 3$ equal to $0$ and solve for $x$ .

Set $2 x - 3$ equal to $0$ .

$2 x - 3 = 0$

Solve $2 x - 3 = 0$ for $x$ .

Add $3$ to both sides of the equation.

$2 x = 3$

Divide each term in $2 x = 3$ by $2$ and simplify.

Divide each term in $2 x = 3$ by $2$ .

$\frac{2 x}{2} = \frac{3}{2}$

Simplify the left side.

Cancel the common factor of $2$ .

Cancel the common factor.

$\frac{2 x}{2} = \frac{3}{2}$

Divide $x$ by $1$ .

$x = \frac{3}{2}$

Step 3

Set $100 x^{2} - 81$ equal to $0$ and solve for $x$ .

Set $100 x^{2} - 81$ equal to $0$ .

$100 x^{2} - 81 = 0$

Solve $100 x^{2} - 81 = 0$ for $x$ .

Add $81$ to both sides of the equation.

$100 x^{2} = 81$

Divide each term in $100 x^{2} = 81$ by $100$ and simplify.

Divide each term in $100 x^{2} = 81$ by $100$ .

$\frac{100 x^{2}}{100} = \frac{81}{100}$

Simplify the left side.

Cancel the common factor of $100$ .

Cancel the common factor.

$\frac{100 x^{2}}{100} = \frac{81}{100}$

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

$x^{2} = \frac{81}{100}$

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

$x = \pm \sqrt{\frac{81}{100}}$

Simplify $\pm \sqrt{\frac{81}{100}}$ .

Rewrite $\sqrt{\frac{81}{100}}$ as $\frac{\sqrt{81}}{\sqrt{100}}$ .

$x = \pm \frac{\sqrt{81}}{\sqrt{100}}$

Simplify the numerator.

Rewrite $81$ as $9^{2}$ .

$x = \pm \frac{\sqrt{9^{2}}}{\sqrt{100}}$

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

$x = \pm \frac{9}{\sqrt{100}}$

Simplify the denominator.

Rewrite $100$ as $10^{2}$ .

$x = \pm \frac{9}{\sqrt{10^{2}}}$

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

$x = \pm \frac{9}{10}$

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.

$x = \frac{9}{10}$

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

$x = - \frac{9}{10}$

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

$x = \frac{9}{10}, - \frac{9}{10}$

Step 4

The final solution is all the values that make $2 (2 x - 3) (100 x^{2} - 81) = 0$ true.

$x = \frac{3}{2}, \frac{9}{10}, - \frac{9}{10}$

Step 5

The result can be shown in multiple forms.

Exact Form:

$x = \frac{3}{2}, \frac{9}{10}, - \frac{9}{10}$

Decimal Form:

$x = 1.5, 0.9, - 0.9$

Mixed Number Form:

$x = 1 \frac{1}{2}, \frac{9}{10}, - \frac{9}{10}$

Solve for x 2(2x-3)(100x^2-81)=0

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