(5y-21)(2y-6)=180

Solution for (5y-21)(2y-6)=180 equation:

Simplifying
(5y + -21)(2y + -6) = 180

Reorder the terms:
(-21 + 5y)(2y + -6) = 180

Reorder the terms:
(-21 + 5y)(-6 + 2y) = 180

Multiply (-21 + 5y) * (-6 + 2y)
(-21(-6 + 2y) + 5y * (-6 + 2y)) = 180
((-6 * -21 + 2y * -21) + 5y * (-6 + 2y)) = 180
((126 + -42y) + 5y * (-6 + 2y)) = 180
(126 + -42y + (-6 * 5y + 2y * 5y)) = 180
(126 + -42y + (-30y + 10y2)) = 180

Combine like terms: -42y + -30y = -72y
(126 + -72y + 10y2) = 180

Solving
126 + -72y + 10y2 = 180

Solving for variable 'y'.

Reorder the terms:
126 + -180 + -72y + 10y2 = 180 + -180

Combine like terms: 126 + -180 = -54
-54 + -72y + 10y2 = 180 + -180

Combine like terms: 180 + -180 = 0
-54 + -72y + 10y2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-27 + -36y + 5y2) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(-27 + -36y + 5y2)' equal to zero and attempt to solve:

Simplifying
-27 + -36y + 5y2 = 0

Solving
-27 + -36y + 5y2 = 0

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

Divide each side by '5'.
-5.4 + -7.2y + y2 = 0

Move the constant term to the right:

Add '5.4' to each side of the equation.
-5.4 + -7.2y + 5.4 + y2 = 0 + 5.4

Reorder the terms:
-5.4 + 5.4 + -7.2y + y2 = 0 + 5.4

Combine like terms: -5.4 + 5.4 = 0.0
0.0 + -7.2y + y2 = 0 + 5.4
-7.2y + y2 = 0 + 5.4

Combine like terms: 0 + 5.4 = 5.4
-7.2y + y2 = 5.4

The y term is -7.2y.  Take half its coefficient (-3.6).
Square it (12.96) and add it to both sides.

Add '12.96' to each side of the equation.
-7.2y + 12.96 + y2 = 5.4 + 12.96

Reorder the terms:
12.96 + -7.2y + y2 = 5.4 + 12.96

Combine like terms: 5.4 + 12.96 = 18.36
12.96 + -7.2y + y2 = 18.36

Factor a perfect square on the left side:
(y + -3.6)(y + -3.6) = 18.36

Calculate the square root of the right side: 4.284857057

Break this problem into two subproblems by setting 
(y + -3.6) equal to 4.284857057 and -4.284857057.

Subproblem 1
y + -3.6 = 4.284857057

Simplifying
y + -3.6 = 4.284857057

Reorder the terms:
-3.6 + y = 4.284857057

Solving
-3.6 + y = 4.284857057

Solving for variable 'y'.

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

Add '3.6' to each side of the equation.
-3.6 + 3.6 + y = 4.284857057 + 3.6

Combine like terms: -3.6 + 3.6 = 0.0
0.0 + y = 4.284857057 + 3.6
y = 4.284857057 + 3.6

Combine like terms: 4.284857057 + 3.6 = 7.884857057
y = 7.884857057

Simplifying
y = 7.884857057

Subproblem 2
y + -3.6 = -4.284857057

Simplifying
y + -3.6 = -4.284857057

Reorder the terms:
-3.6 + y = -4.284857057

Solving
-3.6 + y = -4.284857057

Solving for variable 'y'.

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

Add '3.6' to each side of the equation.
-3.6 + 3.6 + y = -4.284857057 + 3.6

Combine like terms: -3.6 + 3.6 = 0.0
0.0 + y = -4.284857057 + 3.6
y = -4.284857057 + 3.6

Combine like terms: -4.284857057 + 3.6 = -0.684857057
y = -0.684857057

Simplifying
y = -0.684857057

Solution
The solution to the problem is based on the solutions
from the subproblems.
y = {7.884857057, -0.684857057}
Solution
y = {7.884857057, -0.684857057}