Solve (t-7)^2=(t+7)^2-84

$$( t - 7 ) ^ { 2 } = ( t + 7 ) ^ { 2 } - 84$$

Solve for t

$$t=3$$

Steps for Solving Linear Equation

Use binomial theorem \left(a-b\right)^{2}=a^{2}-2ab+b^{2} to expand \left(t-7\right)^{2}.

$$t^{2}-14t+49=\left(t+7\right)^{2}-84$$

Use binomial theorem \left(a+b\right)^{2}=a^{2}+2ab+b^{2} to expand \left(t+7\right)^{2}.

$$t^{2}-14t+49=t^{2}+14t+49-84$$

Subtract 84 from 49 to get -35.

$$t^{2}-14t+49=t^{2}+14t-35$$

Subtract t^{2} from both sides.

$$t^{2}-14t+49-t^{2}=14t-35$$

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

$$-14t+49=14t-35$$

Subtract 14t from both sides.

$$-14t+49-14t=-35$$

Combine -14t and -14t to get -28t.

$$-28t+49=-35$$

Subtract 49 from both sides.

$$-28t=-35-49$$

Subtract 49 from -35 to get -84.

$$-28t=-84$$

Divide both sides by -28.

$$t=\frac{-84}{-28}$$

Divide -84 by -28 to get 3.

$$t=3$$