Solve A+2xy^2z=-3xy^2z

$$A + 2 x y ^ { 2 } z = - 3 x y ^ { 2 } z$$

Solve for A

$$A=-5xzy^{2}$$

Solution Steps

Subtract 2xy^{2}z from both sides.

$$A=-3xy^{2}z-2xy^{2}z$$

Combine -3xy^{2}z and -2xy^{2}z to get -5xy^{2}z.

$$A=-5xy^{2}z$$

Solve for x

$$\left\{\begin{matrix}x=-\frac{A}{5zy^{2}}\text{, }&z\neq 0\text{ and }y\neq 0\\x\in \mathrm{R}\text{, }&\left(z=0\text{ or }y=0\right)\text{ and }A=0\end{matrix}\right.$$

Steps for Solving Linear Equation

Add 3xy^{2}z to both sides.

$$A+2xy^{2}z+3xy^{2}z=0$$

Combine 2xy^{2}z and 3xy^{2}z to get 5xy^{2}z.

$$A+5xy^{2}z=0$$

Subtract A from both sides. Anything subtracted from zero gives its negation.

$$5xy^{2}z=-A$$

The equation is in standard form.

$$5zy^{2}x=-A$$

Divide both sides by 5y^{2}z.

$$\frac{5zy^{2}x}{5zy^{2}}=-\frac{A}{5zy^{2}}$$

Dividing by 5y^{2}z undoes the multiplication by 5y^{2}z.

$$x=-\frac{A}{5zy^{2}}$$