Solve (24-2c)(20-x)=320

$$( 24 - 2 c ) ( 20 - x ) = 320$$

Solve for c

$$c=-\frac{4\left(20-3x\right)}{x-20}$$

$$x\neq 20$$

Steps for Solving Linear Equation

Use the distributive property to multiply 24-2c by 20-x.

$$480-24x-40c+2cx=320$$

Subtract 480 from both sides.

$$-24x-40c+2cx=320-480$$

Subtract 480 from 320 to get -160.

$$-24x-40c+2cx=-160$$

Add 24x to both sides.

$$-40c+2cx=-160+24x$$

Combine all terms containing c.

$$\left(-40+2x\right)c=-160+24x$$

The equation is in standard form.

$$\left(2x-40\right)c=24x-160$$

Divide both sides by -40+2x.

$$\frac{\left(2x-40\right)c}{2x-40}=\frac{24x-160}{2x-40}$$

Dividing by -40+2x undoes the multiplication by -40+2x.

$$c=\frac{24x-160}{2x-40}$$

Divide -160+24x by -40+2x.

$$c=\frac{4\left(3x-20\right)}{x-20}$$

Solve for x

$$x=-\frac{20\left(4-c\right)}{c-12}$$

$$c\neq 12$$

Steps for Solving Linear Equation

Use the distributive property to multiply 24-2c by 20-x.

$$480-24x-40c+2xc=320$$

Subtract 480 from both sides.

$$-24x-40c+2xc=320-480$$

Subtract 480 from 320 to get -160.

$$-24x-40c+2xc=-160$$

Add 40c to both sides.

$$-24x+2xc=-160+40c$$

Combine all terms containing x.

$$\left(-24+2c\right)x=-160+40c$$

The equation is in standard form.

$$\left(2c-24\right)x=40c-160$$

Divide both sides by -24+2c.

$$\frac{\left(2c-24\right)x}{2c-24}=\frac{40c-160}{2c-24}$$

Dividing by -24+2c undoes the multiplication by -24+2c.

$$x=\frac{40c-160}{2c-24}$$

Divide -160+40c by -24+2c.

$$x=\frac{20\left(c-4\right)}{c-12}$$