Solve left(58-yright)*(50-y)=left(50+yright)^2

$$\left( 58-y \right) \times (50-y) = { \left(50+y \right) }^{ 2 }$$

Solve for y

$$y = \frac{25}{13} = 1\frac{12}{13} \approx 1.923076923$$

Steps for Solving Linear Equation

Use the distributive property to multiply 58-y by 50-y and combine like terms.

$$2900-108y+y^{2}=\left(50+y\right)^{2}$$

Use binomial theorem \left(a+b\right)^{2}=a^{2}+2ab+b^{2} to expand \left(50+y\right)^{2}.

$$2900-108y+y^{2}=2500+100y+y^{2}$$

Subtract 100y from both sides.

$$2900-108y+y^{2}-100y=2500+y^{2}$$

Combine -108y and -100y to get -208y.

$$2900-208y+y^{2}=2500+y^{2}$$

Subtract y^{2} from both sides.

$$2900-208y+y^{2}-y^{2}=2500$$

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

$$2900-208y=2500$$

Subtract 2900 from both sides.

$$-208y=2500-2900$$

Subtract 2900 from 2500 to get -400.

$$-208y=-400$$

Divide both sides by -208.

$$y=\frac{-400}{-208}$$

Reduce the fraction \frac{-400}{-208} to lowest terms by extracting and canceling out -16.

$$y=\frac{25}{13}$$