(2y-2)(y-3)-(3y+2)(4y-1)=

Solution for (2y-2)(y-3)-(3y+2)(4y-1)= equation:

Simplifying
(2y + -2)(y + -3) + -1(3y + 2)(4y + -1) = 0

Reorder the terms:
(-2 + 2y)(y + -3) + -1(3y + 2)(4y + -1) = 0

Reorder the terms:
(-2 + 2y)(-3 + y) + -1(3y + 2)(4y + -1) = 0

Multiply (-2 + 2y) * (-3 + y)
(-2(-3 + y) + 2y * (-3 + y)) + -1(3y + 2)(4y + -1) = 0
((-3 * -2 + y * -2) + 2y * (-3 + y)) + -1(3y + 2)(4y + -1) = 0
((6 + -2y) + 2y * (-3 + y)) + -1(3y + 2)(4y + -1) = 0
(6 + -2y + (-3 * 2y + y * 2y)) + -1(3y + 2)(4y + -1) = 0
(6 + -2y + (-6y + 2y2)) + -1(3y + 2)(4y + -1) = 0

Combine like terms: -2y + -6y = -8y
(6 + -8y + 2y2) + -1(3y + 2)(4y + -1) = 0

Reorder the terms:
6 + -8y + 2y2 + -1(2 + 3y)(4y + -1) = 0

Reorder the terms:
6 + -8y + 2y2 + -1(2 + 3y)(-1 + 4y) = 0

Multiply (2 + 3y) * (-1 + 4y)
6 + -8y + 2y2 + -1(2(-1 + 4y) + 3y * (-1 + 4y)) = 0
6 + -8y + 2y2 + -1((-1 * 2 + 4y * 2) + 3y * (-1 + 4y)) = 0
6 + -8y + 2y2 + -1((-2 + 8y) + 3y * (-1 + 4y)) = 0
6 + -8y + 2y2 + -1(-2 + 8y + (-1 * 3y + 4y * 3y)) = 0
6 + -8y + 2y2 + -1(-2 + 8y + (-3y + 12y2)) = 0

Combine like terms: 8y + -3y = 5y
6 + -8y + 2y2 + -1(-2 + 5y + 12y2) = 0
6 + -8y + 2y2 + (-2 * -1 + 5y * -1 + 12y2 * -1) = 0
6 + -8y + 2y2 + (2 + -5y + -12y2) = 0

Reorder the terms:
6 + 2 + -8y + -5y + 2y2 + -12y2 = 0

Combine like terms: 6 + 2 = 8
8 + -8y + -5y + 2y2 + -12y2 = 0

Combine like terms: -8y + -5y = -13y
8 + -13y + 2y2 + -12y2 = 0

Combine like terms: 2y2 + -12y2 = -10y2
8 + -13y + -10y2 = 0

Solving
8 + -13y + -10y2 = 0

Solving for variable 'y'.

Begin completing the square.  Divide all terms by
-10 the coefficient of the squared term: 

Divide each side by '-10'.
-0.8 + 1.3y + y2 = 0.0

Move the constant term to the right:

Add '0.8' to each side of the equation.
-0.8 + 1.3y + 0.8 + y2 = 0.0 + 0.8

Reorder the terms:
-0.8 + 0.8 + 1.3y + y2 = 0.0 + 0.8

Combine like terms: -0.8 + 0.8 = 0.0
0.0 + 1.3y + y2 = 0.0 + 0.8
1.3y + y2 = 0.0 + 0.8

Combine like terms: 0.0 + 0.8 = 0.8
1.3y + y2 = 0.8

The y term is 1.3y.  Take half its coefficient (0.65).
Square it (0.4225) and add it to both sides.

Add '0.4225' to each side of the equation.
1.3y + 0.4225 + y2 = 0.8 + 0.4225

Reorder the terms:
0.4225 + 1.3y + y2 = 0.8 + 0.4225

Combine like terms: 0.8 + 0.4225 = 1.2225
0.4225 + 1.3y + y2 = 1.2225

Factor a perfect square on the left side:
(y + 0.65)(y + 0.65) = 1.2225

Calculate the square root of the right side: 1.105667219

Break this problem into two subproblems by setting 
(y + 0.65) equal to 1.105667219 and -1.105667219.

Subproblem 1
y + 0.65 = 1.105667219

Simplifying
y + 0.65 = 1.105667219

Reorder the terms:
0.65 + y = 1.105667219

Solving
0.65 + y = 1.105667219

Solving for variable 'y'.

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

Add '-0.65' to each side of the equation.
0.65 + -0.65 + y = 1.105667219 + -0.65

Combine like terms: 0.65 + -0.65 = 0.00
0.00 + y = 1.105667219 + -0.65
y = 1.105667219 + -0.65

Combine like terms: 1.105667219 + -0.65 = 0.455667219
y = 0.455667219

Simplifying
y = 0.455667219

Subproblem 2
y + 0.65 = -1.105667219

Simplifying
y + 0.65 = -1.105667219

Reorder the terms:
0.65 + y = -1.105667219

Solving
0.65 + y = -1.105667219

Solving for variable 'y'.

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

Add '-0.65' to each side of the equation.
0.65 + -0.65 + y = -1.105667219 + -0.65

Combine like terms: 0.65 + -0.65 = 0.00
0.00 + y = -1.105667219 + -0.65
y = -1.105667219 + -0.65

Combine like terms: -1.105667219 + -0.65 = -1.755667219
y = -1.755667219

Simplifying
y = -1.755667219

Solution
The solution to the problem is based on the solutions
from the subproblems.
y = {0.455667219, -1.755667219}