Solve (6-a)(14-a)=(8-a)^2

$$( 6 - a ) ( 14 - a ) = ( 8 - a ) ^ { 2 }$$

Solve for a

$$a=5$$

Steps for Solving Linear Equation

Use the distributive property to multiply 6-a by 14-a and combine like terms.

$$84-20a+a^{2}=\left(8-a\right)^{2}$$

Use binomial theorem \left(a-b\right)^{2}=a^{2}-2ab+b^{2} to expand \left(8-a\right)^{2}.

$$84-20a+a^{2}=64-16a+a^{2}$$

Add 16a to both sides.

$$84-20a+a^{2}+16a=64+a^{2}$$

Combine -20a and 16a to get -4a.

$$84-4a+a^{2}=64+a^{2}$$

Subtract a^{2} from both sides.

$$84-4a+a^{2}-a^{2}=64$$

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

$$84-4a=64$$

Subtract 84 from both sides.

$$-4a=64-84$$

Subtract 84 from 64 to get -20.

$$-4a=-20$$

Divide both sides by -4.

$$a=\frac{-20}{-4}$$

Divide -20 by -4 to get 5.

$$a=5$$