Solve ad^2+bc^2=0

$$a d ^ { 2 } + b c ^ { 2 } = 0$$

Solve for a

$$\left\{\begin{matrix}a=-\left(\frac{c}{d}\right)^{2}b\text{, }&d\neq 0\\a\in \mathrm{R}\text{, }&\left(b=0\text{ or }c=0\right)\text{ and }d=0\end{matrix}\right.$$

Steps for Solving Linear Equation

Subtract bc^{2} from both sides. Anything subtracted from zero gives its negation.

$$ad^{2}=-bc^{2}$$

The equation is in standard form.

$$d^{2}a=-bc^{2}$$

Divide both sides by d^{2}.

$$\frac{d^{2}a}{d^{2}}=-\frac{bc^{2}}{d^{2}}$$

Dividing by d^{2} undoes the multiplication by d^{2}.

$$a=-\frac{bc^{2}}{d^{2}}$$

Solve for b

$$\left\{\begin{matrix}b=-\left(\frac{d}{c}\right)^{2}a\text{, }&c\neq 0\\b\in \mathrm{R}\text{, }&\left(a=0\text{ or }d=0\right)\text{ and }c=0\end{matrix}\right.$$

Steps for Solving Linear Equation

Subtract ad^{2} from both sides. Anything subtracted from zero gives its negation.

$$bc^{2}=-ad^{2}$$

The equation is in standard form.

$$c^{2}b=-ad^{2}$$

Divide both sides by c^{2}.

$$\frac{c^{2}b}{c^{2}}=-\frac{ad^{2}}{c^{2}}$$

Dividing by c^{2} undoes the multiplication by c^{2}.

$$b=-\frac{ad^{2}}{c^{2}}$$