4x^2+60x-32=0

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Solution for 4x^2+60x-32=0 equation: 


Simplifying
4x2 + 60x + -32 = 0

Reorder the terms:
-32 + 60x + 4x2 = 0

Solving
-32 + 60x + 4x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '4'.
4(-8 + 15x + x2) = 0

Ignore the factor 4.

Subproblem 1
Set the factor '(-8 + 15x + x2)' equal to zero and attempt to solve:

Simplifying
-8 + 15x + x2 = 0

Solving
-8 + 15x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '8' to each side of the equation.
-8 + 15x + 8 + x2 = 0 + 8

Reorder the terms:
-8 + 8 + 15x + x2 = 0 + 8

Combine like terms: -8 + 8 = 0
0 + 15x + x2 = 0 + 8
15x + x2 = 0 + 8

Combine like terms: 0 + 8 = 8
15x + x2 = 8

The x term is 15x.  Take half its coefficient (7.5).
Square it (56.25) and add it to both sides.

Add '56.25' to each side of the equation.
15x + 56.25 + x2 = 8 + 56.25

Reorder the terms:
56.25 + 15x + x2 = 8 + 56.25

Combine like terms: 8 + 56.25 = 64.25
56.25 + 15x + x2 = 64.25

Factor a perfect square on the left side:
(x + 7.5)(x + 7.5) = 64.25

Calculate the square root of the right side: 8.015609771

Break this problem into two subproblems by setting 
(x + 7.5) equal to 8.015609771 and -8.015609771.


Subproblem 1
x + 7.5 = 8.015609771

Simplifying
x + 7.5 = 8.015609771

Reorder the terms:
7.5 + x = 8.015609771

Solving
7.5 + x = 8.015609771

Solving for variable 'x'.

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

Add '-7.5' to each side of the equation.
7.5 + -7.5 + x = 8.015609771 + -7.5

Combine like terms: 7.5 + -7.5 = 0.0
0.0 + x = 8.015609771 + -7.5
x = 8.015609771 + -7.5

Combine like terms: 8.015609771 + -7.5 = 0.515609771
x = 0.515609771

Simplifying
x = 0.515609771


Subproblem 2
x + 7.5 = -8.015609771

Simplifying
x + 7.5 = -8.015609771

Reorder the terms:
7.5 + x = -8.015609771

Solving
7.5 + x = -8.015609771

Solving for variable 'x'.

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

Add '-7.5' to each side of the equation.
7.5 + -7.5 + x = -8.015609771 + -7.5

Combine like terms: 7.5 + -7.5 = 0.0
0.0 + x = -8.015609771 + -7.5
x = -8.015609771 + -7.5

Combine like terms: -8.015609771 + -7.5 = -15.515609771
x = -15.515609771

Simplifying
x = -15.515609771


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {0.515609771, -15.515609771}
Solution
x = {0.515609771, -15.515609771}

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