(2y-3)(y-2)-4y^2+12y-9=0

Solution for (2y-3)(y-2)-4y^2+12y-9=0 equation:

Simplifying
(2y + -3)(y + -2) + -4y2 + 12y + -9 = 0

Reorder the terms:
(-3 + 2y)(y + -2) + -4y2 + 12y + -9 = 0

Reorder the terms:
(-3 + 2y)(-2 + y) + -4y2 + 12y + -9 = 0

Multiply (-3 + 2y) * (-2 + y)
(-3(-2 + y) + 2y * (-2 + y)) + -4y2 + 12y + -9 = 0
((-2 * -3 + y * -3) + 2y * (-2 + y)) + -4y2 + 12y + -9 = 0
((6 + -3y) + 2y * (-2 + y)) + -4y2 + 12y + -9 = 0
(6 + -3y + (-2 * 2y + y * 2y)) + -4y2 + 12y + -9 = 0
(6 + -3y + (-4y + 2y2)) + -4y2 + 12y + -9 = 0

Combine like terms: -3y + -4y = -7y
(6 + -7y + 2y2) + -4y2 + 12y + -9 = 0

Reorder the terms:
6 + -9 + -7y + 12y + 2y2 + -4y2 = 0

Combine like terms: 6 + -9 = -3
-3 + -7y + 12y + 2y2 + -4y2 = 0

Combine like terms: -7y + 12y = 5y
-3 + 5y + 2y2 + -4y2 = 0

Combine like terms: 2y2 + -4y2 = -2y2
-3 + 5y + -2y2 = 0

Solving
-3 + 5y + -2y2 = 0

Solving for variable 'y'.

Factor a trinomial.
(-3 + 2y)(1 + -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 '(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
Solution
y = {1.5, 1}