Solve z^2=-3x+7/14yz

$$z ^ { 2 } = \frac { - 3 x + 7 } { 14 y z }$$

Solve for x

$$x=\frac{7-14yz^{3}}{3}$$

$$z\neq 0\text{ and }y\neq 0$$

Steps for Solving Linear Equation

Multiply both sides of the equation by 14yz.

$$14yzz^{2}=-3x+7$$

To multiply powers of the same base, add their exponents. Add 1 and 2 to get 3.

$$14yz^{3}=-3x+7$$

Swap sides so that all variable terms are on the left hand side.

$$-3x+7=14yz^{3}$$

Subtract 7 from both sides.

$$-3x=14yz^{3}-7$$

Divide both sides by -3.

$$\frac{-3x}{-3}=\frac{14yz^{3}-7}{-3}$$

Dividing by -3 undoes the multiplication by -3.

$$x=\frac{14yz^{3}-7}{-3}$$

Divide 14yz^{3}-7 by -3.

$$x=\frac{7-14yz^{3}}{3}$$

Solve for y

$$y=-\frac{3x-7}{14z^{3}}$$

$$x\neq \frac{7}{3}\text{ and }z\neq 0$$

Steps for Solving Linear Equation

Variable y cannot be equal to 0 since division by zero is not defined. Multiply both sides of the equation by 14yz.

$$14yzz^{2}=-3x+7$$

To multiply powers of the same base, add their exponents. Add 1 and 2 to get 3.

$$14yz^{3}=-3x+7$$

The equation is in standard form.

$$14z^{3}y=7-3x$$

Divide both sides by 14z^{3}.

$$\frac{14z^{3}y}{14z^{3}}=\frac{7-3x}{14z^{3}}$$

Dividing by 14z^{3} undoes the multiplication by 14z^{3}.

$$y=\frac{7-3x}{14z^{3}}$$

Variable y cannot be equal to 0.

$$y=\frac{7-3x}{14z^{3}}\text{, }y\neq 0$$