Solve for x (7x+10)(x^2-13)=0

$(7 x + 10) (x^{2} - 13) = 0$

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

$7 x + 10 = 0$

$x^{2} - 13 = 0$

Set $7 x + 10$ equal to $0$ and solve for $x$ .

Set $7 x + 10$ equal to $0$ .

$7 x + 10 = 0$

Solve $7 x + 10 = 0$ for $x$ .

Subtract $10$ from both sides of the equation.

$7 x = - 10$

Divide each term in $7 x = - 10$ by $7$ and simplify.

Divide each term in $7 x = - 10$ by $7$ .

$\frac{7 x}{7} = \frac{- 10}{7}$

Simplify the left side.

Cancel the common factor of $7$ .

Cancel the common factor.

$\frac{7 x}{7} = \frac{- 10}{7}$

Divide $x$ by $1$ .

$x = \frac{- 10}{7}$

Simplify the right side.

Move the negative in front of the fraction.

$x = - \frac{10}{7}$

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.

$x = \sqrt{13}, - \sqrt{13}$

The final solution is all the values that make $(7 x + 10) (x^{2} - 13) = 0$ true.

$x = - \frac{10}{7}, \sqrt{13}, - \sqrt{13}$

The result can be shown in multiple forms.

Exact Form:

$x = - \frac{10}{7}, \sqrt{13}, - \sqrt{13}$

Decimal Form:

$x = - 1.\overline{428571}, 3.60555127 \dots, - 3.60555127 \dots$

Mixed Number Form:

$x = - 1 \frac{3}{7}, \sqrt{13}, - \sqrt{13}$

Solve for x (7x+10)(x^2-13)=0

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