Solve W=15x+(30-m)(40-x)

$$W = 15 x + ( 30 - m ) ( 40 - x )$$

Solve for m (complex solution)

$$\left\{\begin{matrix}m=-\frac{1200-W-15x}{x-40}\text{, }&x\neq 40\\m\in \mathrm{C}\text{, }&W=600\text{ and }x=40\end{matrix}\right.$$

Steps for Solving Linear Equation

Use the distributive property to multiply 30-m by 40-x.

$$W=15x+1200-30x-40m+xm$$

Combine 15x and -30x to get -15x.

$$W=-15x+1200-40m+xm$$

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

$$-15x+1200-40m+xm=W$$

Add 15x to both sides.

$$1200-40m+xm=W+15x$$

Subtract 1200 from both sides.

$$-40m+xm=W+15x-1200$$

Combine all terms containing m.

$$\left(-40+x\right)m=W+15x-1200$$

The equation is in standard form.

$$\left(x-40\right)m=15x+W-1200$$

Divide both sides by x-40.

$$\frac{\left(x-40\right)m}{x-40}=\frac{15x+W-1200}{x-40}$$

Dividing by x-40 undoes the multiplication by x-40.

$$m=\frac{15x+W-1200}{x-40}$$

Solve for W

$$W=mx-15x-40m+1200$$

Solution Steps

Use the distributive property to multiply 30-m by 40-x.

$$W=15x+1200-30x-40m+mx$$

Combine 15x and -30x to get -15x.

$$W=-15x+1200-40m+mx$$

Solve for m

$$\left\{\begin{matrix}m=-\frac{1200-W-15x}{x-40}\text{, }&x\neq 40\\m\in \mathrm{R}\text{, }&W=600\text{ and }x=40\end{matrix}\right.$$

Steps for Solving Linear Equation

Use the distributive property to multiply 30-m by 40-x.

$$W=15x+1200-30x-40m+xm$$

Combine 15x and -30x to get -15x.

$$W=-15x+1200-40m+xm$$

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

$$-15x+1200-40m+xm=W$$

Add 15x to both sides.

$$1200-40m+xm=W+15x$$

Subtract 1200 from both sides.

$$-40m+xm=W+15x-1200$$

Combine all terms containing m.

$$\left(-40+x\right)m=W+15x-1200$$

The equation is in standard form.

$$\left(x-40\right)m=15x+W-1200$$

Divide both sides by x-40.

$$\frac{\left(x-40\right)m}{x-40}=\frac{15x+W-1200}{x-40}$$

Dividing by x-40 undoes the multiplication by x-40.

$$m=\frac{15x+W-1200}{x-40}$$