Solve P=4m(2m-3k)

$$P = 4 m ( 2 m - 3 k )$$

Solve for k

$$\left\{\begin{matrix}k=\frac{2m}{3}-\frac{P}{12m}\text{, }&m\neq 0\\k\in \mathrm{R}\text{, }&P=0\text{ and }m=0\end{matrix}\right.$$

Steps for Solving Linear Equation

Use the distributive property to multiply 4m by 2m-3k.

$$P=8m^{2}-12mk$$

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

$$8m^{2}-12mk=P$$

Subtract 8m^{2} from both sides.

$$-12mk=P-8m^{2}$$

The equation is in standard form.

$$\left(-12m\right)k=P-8m^{2}$$

Divide both sides by -12m.

$$\frac{\left(-12m\right)k}{-12m}=\frac{P-8m^{2}}{-12m}$$

Dividing by -12m undoes the multiplication by -12m.

$$k=\frac{P-8m^{2}}{-12m}$$

Divide P-8m^{2} by -12m.

$$k=\frac{2m}{3}-\frac{P}{12m}$$

Solve for P

$$P=4m\left(2m-3k\right)$$

Solution Steps

Use the distributive property to multiply 4m by 2m-3k.

$$P=8m^{2}-12mk$$