4y(2y-5)=32

Solution for 4y(2y-5)=32 equation:

Simplifying
4y(2y + -5) = 32

Reorder the terms:
4y(-5 + 2y) = 32
(-5 * 4y + 2y * 4y) = 32
(-20y + 8y2) = 32

Solving
-20y + 8y2 = 32

Solving for variable 'y'.

Reorder the terms:
-32 + -20y + 8y2 = 32 + -32

Combine like terms: 32 + -32 = 0
-32 + -20y + 8y2 = 0

Factor out the Greatest Common Factor (GCF), '4'.
4(-8 + -5y + 2y2) = 0

Ignore the factor 4.
Subproblem 1
Set the factor '(-8 + -5y + 2y2)' equal to zero and attempt to solve:

Simplifying
-8 + -5y + 2y2 = 0

Solving
-8 + -5y + 2y2 = 0

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

Divide each side by '2'.
-4 + -2.5y + y2 = 0

Move the constant term to the right:

Add '4' to each side of the equation.
-4 + -2.5y + 4 + y2 = 0 + 4

Reorder the terms:
-4 + 4 + -2.5y + y2 = 0 + 4

Combine like terms: -4 + 4 = 0
0 + -2.5y + y2 = 0 + 4
-2.5y + y2 = 0 + 4

Combine like terms: 0 + 4 = 4
-2.5y + y2 = 4

The y term is -2.5y.  Take half its coefficient (-1.25).
Square it (1.5625) and add it to both sides.

Add '1.5625' to each side of the equation.
-2.5y + 1.5625 + y2 = 4 + 1.5625

Reorder the terms:
1.5625 + -2.5y + y2 = 4 + 1.5625

Combine like terms: 4 + 1.5625 = 5.5625
1.5625 + -2.5y + y2 = 5.5625

Factor a perfect square on the left side:
(y + -1.25)(y + -1.25) = 5.5625

Calculate the square root of the right side: 2.358495283

Break this problem into two subproblems by setting 
(y + -1.25) equal to 2.358495283 and -2.358495283.

Subproblem 1
y + -1.25 = 2.358495283

Simplifying
y + -1.25 = 2.358495283

Reorder the terms:
-1.25 + y = 2.358495283

Solving
-1.25 + y = 2.358495283

Solving for variable 'y'.

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

Add '1.25' to each side of the equation.
-1.25 + 1.25 + y = 2.358495283 + 1.25

Combine like terms: -1.25 + 1.25 = 0.00
0.00 + y = 2.358495283 + 1.25
y = 2.358495283 + 1.25

Combine like terms: 2.358495283 + 1.25 = 3.608495283
y = 3.608495283

Simplifying
y = 3.608495283

Subproblem 2
y + -1.25 = -2.358495283

Simplifying
y + -1.25 = -2.358495283

Reorder the terms:
-1.25 + y = -2.358495283

Solving
-1.25 + y = -2.358495283

Solving for variable 'y'.

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

Add '1.25' to each side of the equation.
-1.25 + 1.25 + y = -2.358495283 + 1.25

Combine like terms: -1.25 + 1.25 = 0.00
0.00 + y = -2.358495283 + 1.25
y = -2.358495283 + 1.25

Combine like terms: -2.358495283 + 1.25 = -1.108495283
y = -1.108495283

Simplifying
y = -1.108495283

Solution
The solution to the problem is based on the solutions
from the subproblems.
y = {3.608495283, -1.108495283}
Solution
y = {3.608495283, -1.108495283}