Solve left(21-yright)^2-y^2=7

$${ \left(21-y \right) }^{ 2 } - { y }^{ 2 } =7$$

Solve for y

$$y = \frac{31}{3} = 10\frac{1}{3} \approx 10.333333333$$

Steps for Solving Linear Equation

Use binomial theorem \left(a-b\right)^{2}=a^{2}-2ab+b^{2} to expand \left(21-y\right)^{2}.

$$441-42y+y^{2}-y^{2}=7$$

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

$$441-42y=7$$

Subtract 441 from both sides.

$$-42y=7-441$$

Subtract 441 from 7 to get -434.

$$-42y=-434$$

Divide both sides by -42.

$$y=\frac{-434}{-42}$$

Reduce the fraction \frac{-434}{-42} to lowest terms by extracting and canceling out -14.

$$y=\frac{31}{3}$$