y(y-2)=2(8-y)

Solution for y(y-2)=2(8-y) equation:

Simplifying
y(y + -2) = 2(8 + -1y)

Reorder the terms:
y(-2 + y) = 2(8 + -1y)
(-2 * y + y * y) = 2(8 + -1y)
(-2y + y2) = 2(8 + -1y)
-2y + y2 = (8 * 2 + -1y * 2)
-2y + y2 = (16 + -2y)

Add '2y' to each side of the equation.
-2y + 2y + y2 = 16 + -2y + 2y

Combine like terms: -2y + 2y = 0
0 + y2 = 16 + -2y + 2y
y2 = 16 + -2y + 2y

Combine like terms: -2y + 2y = 0
y2 = 16 + 0
y2 = 16

Solving
y2 = 16

Solving for variable 'y'.

Move all terms containing y to the left, all other terms to the right.

Simplifying
y2 = 16

Take the square root of each side:
y = {-4, 4}