2y(y-3)=y-6

Solution for 2y(y-3)=y-6 equation:

Simplifying
2y(y + -3) = y + -6

Reorder the terms:
2y(-3 + y) = y + -6
(-3 * 2y + y * 2y) = y + -6
(-6y + 2y2) = y + -6

Reorder the terms:
-6y + 2y2 = -6 + y

Solving
-6y + 2y2 = -6 + y

Solving for variable 'y'.

Reorder the terms:
6 + -6y + -1y + 2y2 = -6 + y + 6 + -1y

Combine like terms: -6y + -1y = -7y
6 + -7y + 2y2 = -6 + y + 6 + -1y

Reorder the terms:
6 + -7y + 2y2 = -6 + 6 + y + -1y

Combine like terms: -6 + 6 = 0
6 + -7y + 2y2 = 0 + y + -1y
6 + -7y + 2y2 = y + -1y

Combine like terms: y + -1y = 0
6 + -7y + 2y2 = 0

Factor a trinomial.
(3 + -2y)(2 + -1y) = 0

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

Simplifying
2 + -1y = 0

Solving
2 + -1y = 0

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

Add '-2' to each side of the equation.
2 + -2 + -1y = 0 + -2

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

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

Divide each side by '-1'.
y = 2

Simplifying
y = 2
Solution
y = {1.5, 2}