(2y+9)(4y-6)=180

Solution for (2y+9)(4y-6)=180 equation:

Simplifying
(2y + 9)(4y + -6) = 180

Reorder the terms:
(9 + 2y)(4y + -6) = 180

Reorder the terms:
(9 + 2y)(-6 + 4y) = 180

Multiply (9 + 2y) * (-6 + 4y)
(9(-6 + 4y) + 2y * (-6 + 4y)) = 180
((-6 * 9 + 4y * 9) + 2y * (-6 + 4y)) = 180
((-54 + 36y) + 2y * (-6 + 4y)) = 180
(-54 + 36y + (-6 * 2y + 4y * 2y)) = 180
(-54 + 36y + (-12y + 8y2)) = 180

Combine like terms: 36y + -12y = 24y
(-54 + 24y + 8y2) = 180

Solving
-54 + 24y + 8y2 = 180

Solving for variable 'y'.

Reorder the terms:
-54 + -180 + 24y + 8y2 = 180 + -180

Combine like terms: -54 + -180 = -234
-234 + 24y + 8y2 = 180 + -180

Combine like terms: 180 + -180 = 0
-234 + 24y + 8y2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-117 + 12y + 4y2) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(-117 + 12y + 4y2)' equal to zero and attempt to solve:

Simplifying
-117 + 12y + 4y2 = 0

Solving
-117 + 12y + 4y2 = 0

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

Divide each side by '4'.
-29.25 + 3y + y2 = 0

Move the constant term to the right:

Add '29.25' to each side of the equation.
-29.25 + 3y + 29.25 + y2 = 0 + 29.25

Reorder the terms:
-29.25 + 29.25 + 3y + y2 = 0 + 29.25

Combine like terms: -29.25 + 29.25 = 0.00
0.00 + 3y + y2 = 0 + 29.25
3y + y2 = 0 + 29.25

Combine like terms: 0 + 29.25 = 29.25
3y + y2 = 29.25

The y term is 3y.  Take half its coefficient (1.5).
Square it (2.25) and add it to both sides.

Add '2.25' to each side of the equation.
3y + 2.25 + y2 = 29.25 + 2.25

Reorder the terms:
2.25 + 3y + y2 = 29.25 + 2.25

Combine like terms: 29.25 + 2.25 = 31.5
2.25 + 3y + y2 = 31.5

Factor a perfect square on the left side:
(y + 1.5)(y + 1.5) = 31.5

Calculate the square root of the right side: 5.61248608

Break this problem into two subproblems by setting 
(y + 1.5) equal to 5.61248608 and -5.61248608.

Subproblem 1
y + 1.5 = 5.61248608

Simplifying
y + 1.5 = 5.61248608

Reorder the terms:
1.5 + y = 5.61248608

Solving
1.5 + y = 5.61248608

Solving for variable 'y'.

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

Add '-1.5' to each side of the equation.
1.5 + -1.5 + y = 5.61248608 + -1.5

Combine like terms: 1.5 + -1.5 = 0.0
0.0 + y = 5.61248608 + -1.5
y = 5.61248608 + -1.5

Combine like terms: 5.61248608 + -1.5 = 4.11248608
y = 4.11248608

Simplifying
y = 4.11248608

Subproblem 2
y + 1.5 = -5.61248608

Simplifying
y + 1.5 = -5.61248608

Reorder the terms:
1.5 + y = -5.61248608

Solving
1.5 + y = -5.61248608

Solving for variable 'y'.

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

Add '-1.5' to each side of the equation.
1.5 + -1.5 + y = -5.61248608 + -1.5

Combine like terms: 1.5 + -1.5 = 0.0
0.0 + y = -5.61248608 + -1.5
y = -5.61248608 + -1.5

Combine like terms: -5.61248608 + -1.5 = -7.11248608
y = -7.11248608

Simplifying
y = -7.11248608

Solution
The solution to the problem is based on the solutions
from the subproblems.
y = {4.11248608, -7.11248608}
Solution
y = {4.11248608, -7.11248608}