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

Solution for 2y(y-1)=5y-5 equation:

Simplifying
2y(y + -1) = 5y + -5

Reorder the terms:
2y(-1 + y) = 5y + -5
(-1 * 2y + y * 2y) = 5y + -5
(-2y + 2y2) = 5y + -5

Reorder the terms:
-2y + 2y2 = -5 + 5y

Solving
-2y + 2y2 = -5 + 5y

Solving for variable 'y'.

Reorder the terms:
5 + -2y + -5y + 2y2 = -5 + 5y + 5 + -5y

Combine like terms: -2y + -5y = -7y
5 + -7y + 2y2 = -5 + 5y + 5 + -5y

Reorder the terms:
5 + -7y + 2y2 = -5 + 5 + 5y + -5y

Combine like terms: -5 + 5 = 0
5 + -7y + 2y2 = 0 + 5y + -5y
5 + -7y + 2y2 = 5y + -5y

Combine like terms: 5y + -5y = 0
5 + -7y + 2y2 = 0

Factor a trinomial.
(1 + -1y)(5 + -2y) = 0

Subproblem 1
Set the factor '(1 + -1y)' equal to zero and attempt to solve:

Simplifying
1 + -1y = 0

Solving
1 + -1y = 0

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

Add '-1' to each side of the equation.
1 + -1 + -1y = 0 + -1

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

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

Divide each side by '-1'.
y = 1

Simplifying
y = 1
Subproblem 2
Set the factor '(5 + -2y)' equal to zero and attempt to solve:

Simplifying
5 + -2y = 0

Solving
5 + -2y = 0

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

Add '-5' to each side of the equation.
5 + -5 + -2y = 0 + -5

Combine like terms: 5 + -5 = 0
0 + -2y = 0 + -5
-2y = 0 + -5

Combine like terms: 0 + -5 = -5
-2y = -5

Divide each side by '-2'.
y = 2.5

Simplifying
y = 2.5
Solution
y = {1, 2.5}