2y(y-1)=3-y

Solution for 2y(y-1)=3-y equation:

Simplifying
2y(y + -1) = 3 + -1y

Reorder the terms:
2y(-1 + y) = 3 + -1y
(-1 * 2y + y * 2y) = 3 + -1y
(-2y + 2y2) = 3 + -1y

Solving
-2y + 2y2 = 3 + -1y

Solving for variable 'y'.

Reorder the terms:
-3 + -2y + y + 2y2 = 3 + -1y + -3 + y

Combine like terms: -2y + y = -1y
-3 + -1y + 2y2 = 3 + -1y + -3 + y

Reorder the terms:
-3 + -1y + 2y2 = 3 + -3 + -1y + y

Combine like terms: 3 + -3 = 0
-3 + -1y + 2y2 = 0 + -1y + y
-3 + -1y + 2y2 = -1y + y

Combine like terms: -1y + y = 0
-3 + -1y + 2y2 = 0

Factor a trinomial.
(-1 + -1y)(3 + -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 '(3 + -2y)' equal to zero and attempt to solve:

Simplifying
3 + -2y = 0

Solving
3 + -2y = 0

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

Add '-3' to each side of the equation.
3 + -3 + -2y = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -2y = 0 + -3
-2y = 0 + -3

Combine like terms: 0 + -3 = -3
-2y = -3

Divide each side by '-2'.
y = 1.5

Simplifying
y = 1.5
Solution
y = {-1, 1.5}