Solve for x -3x(x-10)(81x^2-49)=0

$- 3 x (x - 10) (81 x^{2} - 49) = 0$

Step 1

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

$x = 0$

$x - 10 = 0$

$81 x^{2} - 49 = 0$

Step 2

Set $x$ equal to $0$ .

$x = 0$

Step 3

Set $x - 10$ equal to $0$ and solve for $x$ .

Set $x - 10$ equal to $0$ .

$x - 10 = 0$

Add $10$ to both sides of the equation.

$x = 10$

Step 4

Set $81 x^{2} - 49$ equal to $0$ and solve for $x$ .

Set $81 x^{2} - 49$ equal to $0$ .

$81 x^{2} - 49 = 0$

Solve $81 x^{2} - 49 = 0$ for $x$ .

Add $49$ to both sides of the equation.

$81 x^{2} = 49$

Divide each term in $81 x^{2} = 49$ by $81$ and simplify.

Divide each term in $81 x^{2} = 49$ by $81$ .

$\frac{81 x^{2}}{81} = \frac{49}{81}$

Simplify the left side.

Cancel the common factor of $81$ .

Cancel the common factor.

$\frac{81 x^{2}}{81} = \frac{49}{81}$

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

$x^{2} = \frac{49}{81}$

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

$x = \pm \sqrt{\frac{49}{81}}$

Simplify $\pm \sqrt{\frac{49}{81}}$ .

Rewrite $\sqrt{\frac{49}{81}}$ as $\frac{\sqrt{49}}{\sqrt{81}}$ .

$x = \pm \frac{\sqrt{49}}{\sqrt{81}}$

Simplify the numerator.

Rewrite $49$ as $7^{2}$ .

$x = \pm \frac{\sqrt{7^{2}}}{\sqrt{81}}$

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

$x = \pm \frac{7}{\sqrt{81}}$

Simplify the denominator.

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

$x = \pm \frac{7}{\sqrt{9^{2}}}$

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

$x = \pm \frac{7}{9}$

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.

$x = \frac{7}{9}$

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

$x = - \frac{7}{9}$

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

$x = \frac{7}{9}, - \frac{7}{9}$

Step 5

The final solution is all the values that make $- 3 x (x - 10) (81 x^{2} - 49) = 0$ true.

$x = 0, 10, \frac{7}{9}, - \frac{7}{9}$

Step 6

The result can be shown in multiple forms.

Exact Form:

$x = 0, 10, \frac{7}{9}, - \frac{7}{9}$

Decimal Form:

$x = 0, 10, 0.\overline{7}, - 0.\overline{7}$

Solve for x -3x(x-10)(81x^2-49)=0

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