Solve z=8x(7x+5y)

$$z = 8 x ( 7 x + 5 y )$$

Solve for y (complex solution)

$$\left\{\begin{matrix}y=-\frac{7x}{5}+\frac{z}{40x}\text{, }&x\neq 0\\y\in \mathrm{C}\text{, }&z=0\text{ and }x=0\end{matrix}\right.$$

Steps for Solving Linear Equation

Use the distributive property to multiply 8x by 7x+5y.

$$z=56x^{2}+40yx$$

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

$$56x^{2}+40yx=z$$

Subtract 56x^{2} from both sides.

$$40yx=z-56x^{2}$$

The equation is in standard form.

$$40xy=z-56x^{2}$$

Divide both sides by 40x.

$$\frac{40xy}{40x}=\frac{z-56x^{2}}{40x}$$

Dividing by 40x undoes the multiplication by 40x.

$$y=\frac{z-56x^{2}}{40x}$$

Divide z-56x^{2} by 40x.

$$y=-\frac{7x}{5}+\frac{z}{40x}$$

Solve for y

$$\left\{\begin{matrix}y=-\frac{7x}{5}+\frac{z}{40x}\text{, }&x\neq 0\\y\in \mathrm{R}\text{, }&z=0\text{ and }x=0\end{matrix}\right.$$

Steps for Solving Linear Equation

Use the distributive property to multiply 8x by 7x+5y.

$$z=56x^{2}+40yx$$

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

$$56x^{2}+40yx=z$$

Subtract 56x^{2} from both sides.

$$40yx=z-56x^{2}$$

The equation is in standard form.

$$40xy=z-56x^{2}$$

Divide both sides by 40x.

$$\frac{40xy}{40x}=\frac{z-56x^{2}}{40x}$$

Dividing by 40x undoes the multiplication by 40x.

$$y=\frac{z-56x^{2}}{40x}$$

Divide z-56x^{2} by 40x.

$$y=-\frac{7x}{5}+\frac{z}{40x}$$

Solve for x (complex solution)

$$x=\frac{\sqrt{100y^{2}+14z}}{28}-\frac{5y}{14}$$

$$x=-\frac{\sqrt{100y^{2}+14z}}{28}-\frac{5y}{14}$$

Solve for x

$$x=\frac{\sqrt{100y^{2}+14z}}{28}-\frac{5y}{14}$$

$$x=-\frac{\sqrt{100y^{2}+14z}}{28}-\frac{5y}{14}\text{, }z\geq -\frac{50y^{2}}{7}$$