Solve for z 12z^2=7z^2+20

$12 z^{2} = 7 z^{2} + 20$

Move all terms containing $z$ to the left side of the equation.

Subtract $7 z^{2}$ from both sides of the equation.

$12 z^{2} - 7 z^{2} = 20$

Subtract $7 z^{2}$ from $12 z^{2}$ .

$5 z^{2} = 20$

Divide each term in $5 z^{2} = 20$ by $5$ and simplify.

Divide each term in $5 z^{2} = 20$ by $5$ .

$\frac{5 z^{2}}{5} = \frac{20}{5}$

Simplify the left side.

Cancel the common factor of $5$ .

Cancel the common factor.

$\frac{5 z^{2}}{5} = \frac{20}{5}$

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

$z^{2} = \frac{20}{5}$

Simplify the right side.

Divide $20$ by $5$ .

$z^{2} = 4$

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

$z = \pm \sqrt{4}$

Simplify $\pm \sqrt{4}$ .

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

$z = \pm \sqrt{2^{2}}$

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

$z = \pm 2$

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.

$z = 2$

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

$z = - 2$

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

$z = 2, - 2$