(3y-20)(4y+4)=180

Solution for (3y-20)(4y+4)=180 equation:

Simplifying
(3y + -20)(4y + 4) = 180

Reorder the terms:
(-20 + 3y)(4y + 4) = 180

Reorder the terms:
(-20 + 3y)(4 + 4y) = 180

Multiply (-20 + 3y) * (4 + 4y)
(-20(4 + 4y) + 3y * (4 + 4y)) = 180
((4 * -20 + 4y * -20) + 3y * (4 + 4y)) = 180
((-80 + -80y) + 3y * (4 + 4y)) = 180
(-80 + -80y + (4 * 3y + 4y * 3y)) = 180
(-80 + -80y + (12y + 12y2)) = 180

Combine like terms: -80y + 12y = -68y
(-80 + -68y + 12y2) = 180

Solving
-80 + -68y + 12y2 = 180

Solving for variable 'y'.

Reorder the terms:
-80 + -180 + -68y + 12y2 = 180 + -180

Combine like terms: -80 + -180 = -260
-260 + -68y + 12y2 = 180 + -180

Combine like terms: 180 + -180 = 0
-260 + -68y + 12y2 = 0

Factor out the Greatest Common Factor (GCF), '4'.
4(-65 + -17y + 3y2) = 0

Ignore the factor 4.
Subproblem 1
Set the factor '(-65 + -17y + 3y2)' equal to zero and attempt to solve:

Simplifying
-65 + -17y + 3y2 = 0

Solving
-65 + -17y + 3y2 = 0

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

Divide each side by '3'.
-21.66666667 + -5.666666667y + y2 = 0

Move the constant term to the right:

Add '21.66666667' to each side of the equation.
-21.66666667 + -5.666666667y + 21.66666667 + y2 = 0 + 21.66666667

Reorder the terms:
-21.66666667 + 21.66666667 + -5.666666667y + y2 = 0 + 21.66666667

Combine like terms: -21.66666667 + 21.66666667 = 0.00000000
0.00000000 + -5.666666667y + y2 = 0 + 21.66666667
-5.666666667y + y2 = 0 + 21.66666667

Combine like terms: 0 + 21.66666667 = 21.66666667
-5.666666667y + y2 = 21.66666667

The y term is -5.666666667y.  Take half its coefficient (-2.833333334).
Square it (8.027777782) and add it to both sides.

Add '8.027777782' to each side of the equation.
-5.666666667y + 8.027777782 + y2 = 21.66666667 + 8.027777782

Reorder the terms:
8.027777782 + -5.666666667y + y2 = 21.66666667 + 8.027777782

Combine like terms: 21.66666667 + 8.027777782 = 29.694444452
8.027777782 + -5.666666667y + y2 = 29.694444452

Factor a perfect square on the left side:
(y + -2.833333334)(y + -2.833333334) = 29.694444452

Calculate the square root of the right side: 5.449260909

Break this problem into two subproblems by setting 
(y + -2.833333334) equal to 5.449260909 and -5.449260909.

Subproblem 1
y + -2.833333334 = 5.449260909

Simplifying
y + -2.833333334 = 5.449260909

Reorder the terms:
-2.833333334 + y = 5.449260909

Solving
-2.833333334 + y = 5.449260909

Solving for variable 'y'.

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

Add '2.833333334' to each side of the equation.
-2.833333334 + 2.833333334 + y = 5.449260909 + 2.833333334

Combine like terms: -2.833333334 + 2.833333334 = 0.000000000
0.000000000 + y = 5.449260909 + 2.833333334
y = 5.449260909 + 2.833333334

Combine like terms: 5.449260909 + 2.833333334 = 8.282594243
y = 8.282594243

Simplifying
y = 8.282594243

Subproblem 2
y + -2.833333334 = -5.449260909

Simplifying
y + -2.833333334 = -5.449260909

Reorder the terms:
-2.833333334 + y = -5.449260909

Solving
-2.833333334 + y = -5.449260909

Solving for variable 'y'.

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

Add '2.833333334' to each side of the equation.
-2.833333334 + 2.833333334 + y = -5.449260909 + 2.833333334

Combine like terms: -2.833333334 + 2.833333334 = 0.000000000
0.000000000 + y = -5.449260909 + 2.833333334
y = -5.449260909 + 2.833333334

Combine like terms: -5.449260909 + 2.833333334 = -2.615927575
y = -2.615927575

Simplifying
y = -2.615927575

Solution
The solution to the problem is based on the solutions
from the subproblems.
y = {8.282594243, -2.615927575}
Solution
y = {8.282594243, -2.615927575}