(90-2y)(27+8y)=20

Solution for (90-2y)(27+8y)=20 equation:

Simplifying
(90 + -2y)(27 + 8y) = 20

Multiply (90 + -2y) * (27 + 8y)
(90(27 + 8y) + -2y * (27 + 8y)) = 20
((27 * 90 + 8y * 90) + -2y * (27 + 8y)) = 20
((2430 + 720y) + -2y * (27 + 8y)) = 20
(2430 + 720y + (27 * -2y + 8y * -2y)) = 20
(2430 + 720y + (-54y + -16y2)) = 20

Combine like terms: 720y + -54y = 666y
(2430 + 666y + -16y2) = 20

Solving
2430 + 666y + -16y2 = 20

Solving for variable 'y'.

Reorder the terms:
2430 + -20 + 666y + -16y2 = 20 + -20

Combine like terms: 2430 + -20 = 2410
2410 + 666y + -16y2 = 20 + -20

Combine like terms: 20 + -20 = 0
2410 + 666y + -16y2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(1205 + 333y + -8y2) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(1205 + 333y + -8y2)' equal to zero and attempt to solve:

Simplifying
1205 + 333y + -8y2 = 0

Solving
1205 + 333y + -8y2 = 0

Begin completing the square.  Divide all terms by
-8 the coefficient of the squared term: 

Divide each side by '-8'.
-150.625 + -41.625y + y2 = 0

Move the constant term to the right:

Add '150.625' to each side of the equation.
-150.625 + -41.625y + 150.625 + y2 = 0 + 150.625

Reorder the terms:
-150.625 + 150.625 + -41.625y + y2 = 0 + 150.625

Combine like terms: -150.625 + 150.625 = 0.000
0.000 + -41.625y + y2 = 0 + 150.625
-41.625y + y2 = 0 + 150.625

Combine like terms: 0 + 150.625 = 150.625
-41.625y + y2 = 150.625

The y term is -41.625y.  Take half its coefficient (-20.8125).
Square it (433.1601563) and add it to both sides.

Add '433.1601563' to each side of the equation.
-41.625y + 433.1601563 + y2 = 150.625 + 433.1601563

Reorder the terms:
433.1601563 + -41.625y + y2 = 150.625 + 433.1601563

Combine like terms: 150.625 + 433.1601563 = 583.7851563
433.1601563 + -41.625y + y2 = 583.7851563

Factor a perfect square on the left side:
(y + -20.8125)(y + -20.8125) = 583.7851563

Calculate the square root of the right side: 24.161646391

Break this problem into two subproblems by setting 
(y + -20.8125) equal to 24.161646391 and -24.161646391.

Subproblem 1
y + -20.8125 = 24.161646391

Simplifying
y + -20.8125 = 24.161646391

Reorder the terms:
-20.8125 + y = 24.161646391

Solving
-20.8125 + y = 24.161646391

Solving for variable 'y'.

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

Add '20.8125' to each side of the equation.
-20.8125 + 20.8125 + y = 24.161646391 + 20.8125

Combine like terms: -20.8125 + 20.8125 = 0.0000
0.0000 + y = 24.161646391 + 20.8125
y = 24.161646391 + 20.8125

Combine like terms: 24.161646391 + 20.8125 = 44.974146391
y = 44.974146391

Simplifying
y = 44.974146391

Subproblem 2
y + -20.8125 = -24.161646391

Simplifying
y + -20.8125 = -24.161646391

Reorder the terms:
-20.8125 + y = -24.161646391

Solving
-20.8125 + y = -24.161646391

Solving for variable 'y'.

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

Add '20.8125' to each side of the equation.
-20.8125 + 20.8125 + y = -24.161646391 + 20.8125

Combine like terms: -20.8125 + 20.8125 = 0.0000
0.0000 + y = -24.161646391 + 20.8125
y = -24.161646391 + 20.8125

Combine like terms: -24.161646391 + 20.8125 = -3.349146391
y = -3.349146391

Simplifying
y = -3.349146391

Solution
The solution to the problem is based on the solutions
from the subproblems.
y = {44.974146391, -3.349146391}
Solution
y = {44.974146391, -3.349146391}