Solve y(y-1)-(y-5)^2=2

$$y ( y - 1 ) - ( y - 5 ) ^ { 2 } = 2$$

Solve for y

$$y=3$$

Steps for Solving Linear Equation

Use the distributive property to multiply y by y-1.

$$y^{2}-y-\left(y-5\right)^{2}=2$$

Use binomial theorem \left(a-b\right)^{2}=a^{2}-2ab+b^{2} to expand \left(y-5\right)^{2}.

$$y^{2}-y-\left(y^{2}-10y+25\right)=2$$

To find the opposite of y^{2}-10y+25, find the opposite of each term.

$$y^{2}-y-y^{2}+10y-25=2$$

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

$$-y+10y-25=2$$

Combine -y and 10y to get 9y.

$$9y-25=2$$

Add 25 to both sides.

$$9y=2+25$$

Add 2 and 25 to get 27.

$$9y=27$$

Divide both sides by 9.

$$y=\frac{27}{9}$$

Divide 27 by 9 to get 3.

$$y=3$$