(2y-3)(y-2)=-12y+18

Solution for (2y-3)(y-2)=-12y+18 equation:

Simplifying
(2y + -3)(y + -2) = -12y + 18

Reorder the terms:
(-3 + 2y)(y + -2) = -12y + 18

Reorder the terms:
(-3 + 2y)(-2 + y) = -12y + 18

Multiply (-3 + 2y) * (-2 + y)
(-3(-2 + y) + 2y * (-2 + y)) = -12y + 18
((-2 * -3 + y * -3) + 2y * (-2 + y)) = -12y + 18
((6 + -3y) + 2y * (-2 + y)) = -12y + 18
(6 + -3y + (-2 * 2y + y * 2y)) = -12y + 18
(6 + -3y + (-4y + 2y2)) = -12y + 18

Combine like terms: -3y + -4y = -7y
(6 + -7y + 2y2) = -12y + 18

Reorder the terms:
6 + -7y + 2y2 = 18 + -12y

Solving
6 + -7y + 2y2 = 18 + -12y

Solving for variable 'y'.

Reorder the terms:
6 + -18 + -7y + 12y + 2y2 = 18 + -12y + -18 + 12y

Combine like terms: 6 + -18 = -12
-12 + -7y + 12y + 2y2 = 18 + -12y + -18 + 12y

Combine like terms: -7y + 12y = 5y
-12 + 5y + 2y2 = 18 + -12y + -18 + 12y

Reorder the terms:
-12 + 5y + 2y2 = 18 + -18 + -12y + 12y

Combine like terms: 18 + -18 = 0
-12 + 5y + 2y2 = 0 + -12y + 12y
-12 + 5y + 2y2 = -12y + 12y

Combine like terms: -12y + 12y = 0
-12 + 5y + 2y2 = 0

Factor a trinomial.
(-4 + -1y)(3 + -2y) = 0

Subproblem 1
Set the factor '(-4 + -1y)' equal to zero and attempt to solve:

Simplifying
-4 + -1y = 0

Solving
-4 + -1y = 0

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

Add '4' to each side of the equation.
-4 + 4 + -1y = 0 + 4

Combine like terms: -4 + 4 = 0
0 + -1y = 0 + 4
-1y = 0 + 4

Combine like terms: 0 + 4 = 4
-1y = 4

Divide each side by '-1'.
y = -4

Simplifying
y = -4
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 = {-4, 1.5}