Solve (27-x)(8-x)=(7-x)(38-x)

$$(27-x)(8-x)=(7-x)(38-x)$$

Solve for x

$$x=5$$

Steps for Solving Linear Equation

Use the distributive property to multiply 27-x by 8-x and combine like terms.

$$216-35x+x^{2}=\left(7-x\right)\left(38-x\right)$$

Use the distributive property to multiply 7-x by 38-x and combine like terms.

$$216-35x+x^{2}=266-45x+x^{2}$$

Add 45x to both sides.

$$216-35x+x^{2}+45x=266+x^{2}$$

Combine -35x and 45x to get 10x.

$$216+10x+x^{2}=266+x^{2}$$

Subtract x^{2} from both sides.

$$216+10x+x^{2}-x^{2}=266$$

Combine x^{2} and -x^{2} to get 0.

$$216+10x=266$$

Subtract 216 from both sides.

$$10x=266-216$$

Subtract 216 from 266 to get 50.

$$10x=50$$

Divide both sides by 10.

$$x=\frac{50}{10}$$

Divide 50 by 10 to get 5.

$$x=5$$