Solve T^2left(T+Aright)-B=0

$${ T }^{ 2 } \left( T+A \right) -B=0$$

Solve for A (complex solution)

$$\left\{\begin{matrix}A=-T+\frac{B}{T^{2}}\text{, }&T\neq 0\\A\in \mathrm{C}\text{, }&B=0\text{ and }T=0\end{matrix}\right.$$

Steps for Solving Linear Equation

Use the distributive property to multiply T^{2} by T+A.

$$T^{3}+T^{2}A-B=0$$

Subtract T^{3} from both sides. Anything subtracted from zero gives its negation.

$$T^{2}A-B=-T^{3}$$

Add B to both sides.

$$T^{2}A=-T^{3}+B$$

The equation is in standard form.

$$T^{2}A=B-T^{3}$$

Divide both sides by T^{2}.

$$\frac{T^{2}A}{T^{2}}=\frac{B-T^{3}}{T^{2}}$$

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

$$A=\frac{B-T^{3}}{T^{2}}$$

Divide B-T^{3} by T^{2}.

$$A=-T+\frac{B}{T^{2}}$$

Solve for A

$$\left\{\begin{matrix}A=-T+\frac{B}{T^{2}}\text{, }&T\neq 0\\A\in \mathrm{R}\text{, }&B=0\text{ and }T=0\end{matrix}\right.$$

Steps for Solving Linear Equation

Use the distributive property to multiply T^{2} by T+A.

$$T^{3}+T^{2}A-B=0$$

Subtract T^{3} from both sides. Anything subtracted from zero gives its negation.

$$T^{2}A-B=-T^{3}$$

Add B to both sides.

$$T^{2}A=-T^{3}+B$$

The equation is in standard form.

$$T^{2}A=B-T^{3}$$

Divide both sides by T^{2}.

$$\frac{T^{2}A}{T^{2}}=\frac{B-T^{3}}{T^{2}}$$

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

$$A=\frac{B-T^{3}}{T^{2}}$$

Divide B-T^{3} by T^{2}.

$$A=-T+\frac{B}{T^{2}}$$

Solve for B

$$B=\left(A+T\right)T^{2}$$

Steps for Solving Linear Equation

Use the distributive property to multiply T^{2} by T+A.

$$T^{3}+T^{2}A-B=0$$

Subtract T^{3} from both sides. Anything subtracted from zero gives its negation.

$$T^{2}A-B=-T^{3}$$

Subtract T^{2}A from both sides.

$$-B=-T^{3}-T^{2}A$$

Reorder the terms.

$$-B=-AT^{2}-T^{3}$$

Divide both sides by -1.

$$\frac{-B}{-1}=-\frac{\left(A+T\right)T^{2}}{-1}$$

Dividing by -1 undoes the multiplication by -1.

$$B=-\frac{\left(A+T\right)T^{2}}{-1}$$

Divide -\left(A+T\right)T^{2} by -1.

$$B=\left(A+T\right)T^{2}$$