(y-6)(y-2)=(y-4)(y-5)

Solution for (y-6)(y-2)=(y-4)(y-5) equation:

Simplifying
(y + -6)(y + -2) = (y + -4)(y + -5)

Reorder the terms:
(-6 + y)(y + -2) = (y + -4)(y + -5)

Reorder the terms:
(-6 + y)(-2 + y) = (y + -4)(y + -5)

Multiply (-6 + y) * (-2 + y)
(-6(-2 + y) + y(-2 + y)) = (y + -4)(y + -5)
((-2 * -6 + y * -6) + y(-2 + y)) = (y + -4)(y + -5)
((12 + -6y) + y(-2 + y)) = (y + -4)(y + -5)
(12 + -6y + (-2 * y + y * y)) = (y + -4)(y + -5)
(12 + -6y + (-2y + y2)) = (y + -4)(y + -5)

Combine like terms: -6y + -2y = -8y
(12 + -8y + y2) = (y + -4)(y + -5)

Reorder the terms:
12 + -8y + y2 = (-4 + y)(y + -5)

Reorder the terms:
12 + -8y + y2 = (-4 + y)(-5 + y)

Multiply (-4 + y) * (-5 + y)
12 + -8y + y2 = (-4(-5 + y) + y(-5 + y))
12 + -8y + y2 = ((-5 * -4 + y * -4) + y(-5 + y))
12 + -8y + y2 = ((20 + -4y) + y(-5 + y))
12 + -8y + y2 = (20 + -4y + (-5 * y + y * y))
12 + -8y + y2 = (20 + -4y + (-5y + y2))

Combine like terms: -4y + -5y = -9y
12 + -8y + y2 = (20 + -9y + y2)

Add '-1y2' to each side of the equation.
12 + -8y + y2 + -1y2 = 20 + -9y + y2 + -1y2

Combine like terms: y2 + -1y2 = 0
12 + -8y + 0 = 20 + -9y + y2 + -1y2
12 + -8y = 20 + -9y + y2 + -1y2

Combine like terms: y2 + -1y2 = 0
12 + -8y = 20 + -9y + 0
12 + -8y = 20 + -9y

Solving
12 + -8y = 20 + -9y

Solving for variable 'y'.

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

Add '9y' to each side of the equation.
12 + -8y + 9y = 20 + -9y + 9y

Combine like terms: -8y + 9y = 1y
12 + 1y = 20 + -9y + 9y

Combine like terms: -9y + 9y = 0
12 + 1y = 20 + 0
12 + 1y = 20

Add '-12' to each side of the equation.
12 + -12 + 1y = 20 + -12

Combine like terms: 12 + -12 = 0
0 + 1y = 20 + -12
1y = 20 + -12

Combine like terms: 20 + -12 = 8
1y = 8

Divide each side by '1'.
y = 8

Simplifying
y = 8