4q^2+32q-12=0

Solution for 4q^2+32q-12=0 equation:

Simplifying
4q2 + 32q + -12 = 0

Reorder the terms:
-12 + 32q + 4q2 = 0

Solving
-12 + 32q + 4q2 = 0

Solving for variable 'q'.

Factor out the Greatest Common Factor (GCF), '4'.
4(-3 + 8q + q2) = 0

Ignore the factor 4.
Subproblem 1
Set the factor '(-3 + 8q + q2)' equal to zero and attempt to solve:

Simplifying
-3 + 8q + q2 = 0

Solving
-3 + 8q + q2 = 0

Begin completing the square.

Move the constant term to the right:

Add '3' to each side of the equation.
-3 + 8q + 3 + q2 = 0 + 3

Reorder the terms:
-3 + 3 + 8q + q2 = 0 + 3

Combine like terms: -3 + 3 = 0
0 + 8q + q2 = 0 + 3
8q + q2 = 0 + 3

Combine like terms: 0 + 3 = 3
8q + q2 = 3

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

Add '16' to each side of the equation.
8q + 16 + q2 = 3 + 16

Reorder the terms:
16 + 8q + q2 = 3 + 16

Combine like terms: 3 + 16 = 19
16 + 8q + q2 = 19

Factor a perfect square on the left side:
(q + 4)(q + 4) = 19

Calculate the square root of the right side: 4.358898944

Break this problem into two subproblems by setting 
(q + 4) equal to 4.358898944 and -4.358898944.

Subproblem 1
q + 4 = 4.358898944

Simplifying
q + 4 = 4.358898944

Reorder the terms:
4 + q = 4.358898944

Solving
4 + q = 4.358898944

Solving for variable 'q'.

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

Add '-4' to each side of the equation.
4 + -4 + q = 4.358898944 + -4

Combine like terms: 4 + -4 = 0
0 + q = 4.358898944 + -4
q = 4.358898944 + -4

Combine like terms: 4.358898944 + -4 = 0.358898944
q = 0.358898944

Simplifying
q = 0.358898944

Subproblem 2
q + 4 = -4.358898944

Simplifying
q + 4 = -4.358898944

Reorder the terms:
4 + q = -4.358898944

Solving
4 + q = -4.358898944

Solving for variable 'q'.

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

Add '-4' to each side of the equation.
4 + -4 + q = -4.358898944 + -4

Combine like terms: 4 + -4 = 0
0 + q = -4.358898944 + -4
q = -4.358898944 + -4

Combine like terms: -4.358898944 + -4 = -8.358898944
q = -8.358898944

Simplifying
q = -8.358898944

Solution
The solution to the problem is based on the solutions
from the subproblems.
q = {0.358898944, -8.358898944}
Solution
q = {0.358898944, -8.358898944}