3y(2y-5)-(3y-2)(4y+4)=

Solution for 3y(2y-5)-(3y-2)(4y+4)= equation:

Simplifying
3y(2y + -5) + -1(3y + -2)(4y + 4) = 0

Reorder the terms:
3y(-5 + 2y) + -1(3y + -2)(4y + 4) = 0
(-5 * 3y + 2y * 3y) + -1(3y + -2)(4y + 4) = 0
(-15y + 6y2) + -1(3y + -2)(4y + 4) = 0

Reorder the terms:
-15y + 6y2 + -1(-2 + 3y)(4y + 4) = 0

Reorder the terms:
-15y + 6y2 + -1(-2 + 3y)(4 + 4y) = 0

Multiply (-2 + 3y) * (4 + 4y)
-15y + 6y2 + -1(-2(4 + 4y) + 3y * (4 + 4y)) = 0
-15y + 6y2 + -1((4 * -2 + 4y * -2) + 3y * (4 + 4y)) = 0
-15y + 6y2 + -1((-8 + -8y) + 3y * (4 + 4y)) = 0
-15y + 6y2 + -1(-8 + -8y + (4 * 3y + 4y * 3y)) = 0
-15y + 6y2 + -1(-8 + -8y + (12y + 12y2)) = 0

Combine like terms: -8y + 12y = 4y
-15y + 6y2 + -1(-8 + 4y + 12y2) = 0
-15y + 6y2 + (-8 * -1 + 4y * -1 + 12y2 * -1) = 0
-15y + 6y2 + (8 + -4y + -12y2) = 0

Reorder the terms:
8 + -15y + -4y + 6y2 + -12y2 = 0

Combine like terms: -15y + -4y = -19y
8 + -19y + 6y2 + -12y2 = 0

Combine like terms: 6y2 + -12y2 = -6y2
8 + -19y + -6y2 = 0

Solving
8 + -19y + -6y2 = 0

Solving for variable 'y'.

Begin completing the square.  Divide all terms by
-6 the coefficient of the squared term: 

Divide each side by '-6'.
-1.333333333 + 3.166666667y + y2 = 0

Move the constant term to the right:

Add '1.333333333' to each side of the equation.
-1.333333333 + 3.166666667y + 1.333333333 + y2 = 0 + 1.333333333

Reorder the terms:
-1.333333333 + 1.333333333 + 3.166666667y + y2 = 0 + 1.333333333

Combine like terms: -1.333333333 + 1.333333333 = 0.000000000
0.000000000 + 3.166666667y + y2 = 0 + 1.333333333
3.166666667y + y2 = 0 + 1.333333333

Combine like terms: 0 + 1.333333333 = 1.333333333
3.166666667y + y2 = 1.333333333

The y term is 3.166666667y.  Take half its coefficient (1.583333334).
Square it (2.506944447) and add it to both sides.

Add '2.506944447' to each side of the equation.
3.166666667y + 2.506944447 + y2 = 1.333333333 + 2.506944447

Reorder the terms:
2.506944447 + 3.166666667y + y2 = 1.333333333 + 2.506944447

Combine like terms: 1.333333333 + 2.506944447 = 3.84027778
2.506944447 + 3.166666667y + y2 = 3.84027778

Factor a perfect square on the left side:
(y + 1.583333334)(y + 1.583333334) = 3.84027778

Calculate the square root of the right side: 1.95966267

Break this problem into two subproblems by setting 
(y + 1.583333334) equal to 1.95966267 and -1.95966267.

Subproblem 1
y + 1.583333334 = 1.95966267

Simplifying
y + 1.583333334 = 1.95966267

Reorder the terms:
1.583333334 + y = 1.95966267

Solving
1.583333334 + y = 1.95966267

Solving for variable 'y'.

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

Add '-1.583333334' to each side of the equation.
1.583333334 + -1.583333334 + y = 1.95966267 + -1.583333334

Combine like terms: 1.583333334 + -1.583333334 = 0.000000000
0.000000000 + y = 1.95966267 + -1.583333334
y = 1.95966267 + -1.583333334

Combine like terms: 1.95966267 + -1.583333334 = 0.376329336
y = 0.376329336

Simplifying
y = 0.376329336

Subproblem 2
y + 1.583333334 = -1.95966267

Simplifying
y + 1.583333334 = -1.95966267

Reorder the terms:
1.583333334 + y = -1.95966267

Solving
1.583333334 + y = -1.95966267

Solving for variable 'y'.

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

Add '-1.583333334' to each side of the equation.
1.583333334 + -1.583333334 + y = -1.95966267 + -1.583333334

Combine like terms: 1.583333334 + -1.583333334 = 0.000000000
0.000000000 + y = -1.95966267 + -1.583333334
y = -1.95966267 + -1.583333334

Combine like terms: -1.95966267 + -1.583333334 = -3.542996004
y = -3.542996004

Simplifying
y = -3.542996004

Solution
The solution to the problem is based on the solutions
from the subproblems.
y = {0.376329336, -3.542996004}