-4y^2+32y+64=0

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Solution for -4y^2+32y+64=0 equation: 


Simplifying
-4y2 + 32y + 64 = 0

Reorder the terms:
64 + 32y + -4y2 = 0

Solving
64 + 32y + -4y2 = 0

Solving for variable 'y'.

Factor out the Greatest Common Factor (GCF), '4'.
4(16 + 8y + -1y2) = 0

Ignore the factor 4.

Subproblem 1
Set the factor '(16 + 8y + -1y2)' equal to zero and attempt to solve:

Simplifying
16 + 8y + -1y2 = 0

Solving
16 + 8y + -1y2 = 0

Begin completing the square.  Divide all terms by
-1 the coefficient of the squared term: 

Divide each side by '-1'.
-16 + -8y + y2 = 0

Move the constant term to the right:

Add '16' to each side of the equation.
-16 + -8y + 16 + y2 = 0 + 16

Reorder the terms:
-16 + 16 + -8y + y2 = 0 + 16

Combine like terms: -16 + 16 = 0
0 + -8y + y2 = 0 + 16
-8y + y2 = 0 + 16

Combine like terms: 0 + 16 = 16
-8y + y2 = 16

The y term is -8y.  Take half its coefficient (-4).
Square it (16) and add it to both sides.

Add '16' to each side of the equation.
-8y + 16 + y2 = 16 + 16

Reorder the terms:
16 + -8y + y2 = 16 + 16

Combine like terms: 16 + 16 = 32
16 + -8y + y2 = 32

Factor a perfect square on the left side:
(y + -4)(y + -4) = 32

Calculate the square root of the right side: 5.656854249

Break this problem into two subproblems by setting 
(y + -4) equal to 5.656854249 and -5.656854249.


Subproblem 1
y + -4 = 5.656854249

Simplifying
y + -4 = 5.656854249

Reorder the terms:
-4 + y = 5.656854249

Solving
-4 + y = 5.656854249

Solving for variable 'y'.

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

Add '4' to each side of the equation.
-4 + 4 + y = 5.656854249 + 4

Combine like terms: -4 + 4 = 0
0 + y = 5.656854249 + 4
y = 5.656854249 + 4

Combine like terms: 5.656854249 + 4 = 9.656854249
y = 9.656854249

Simplifying
y = 9.656854249


Subproblem 2
y + -4 = -5.656854249

Simplifying
y + -4 = -5.656854249

Reorder the terms:
-4 + y = -5.656854249

Solving
-4 + y = -5.656854249

Solving for variable 'y'.

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

Add '4' to each side of the equation.
-4 + 4 + y = -5.656854249 + 4

Combine like terms: -4 + 4 = 0
0 + y = -5.656854249 + 4
y = -5.656854249 + 4

Combine like terms: -5.656854249 + 4 = -1.656854249
y = -1.656854249

Simplifying
y = -1.656854249


Solution
The solution to the problem is based on the solutions
from the subproblems.
y = {9.656854249, -1.656854249}
Solution
y = {9.656854249, -1.656854249}

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