-2q^2-30q+12=0

Solution for -2q^2-30q+12=0 equation:

Simplifying
-2q2 + -30q + 12 = 0

Reorder the terms:
12 + -30q + -2q2 = 0

Solving
12 + -30q + -2q2 = 0

Solving for variable 'q'.

Factor out the Greatest Common Factor (GCF), '2'.
2(6 + -15q + -1q2) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(6 + -15q + -1q2)' equal to zero and attempt to solve:

Simplifying
6 + -15q + -1q2 = 0

Solving
6 + -15q + -1q2 = 0

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

Divide each side by '-1'.
-6 + 15q + q2 = 0

Move the constant term to the right:

Add '6' to each side of the equation.
-6 + 15q + 6 + q2 = 0 + 6

Reorder the terms:
-6 + 6 + 15q + q2 = 0 + 6

Combine like terms: -6 + 6 = 0
0 + 15q + q2 = 0 + 6
15q + q2 = 0 + 6

Combine like terms: 0 + 6 = 6
15q + q2 = 6

The q term is 15q.  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.
15q + 56.25 + q2 = 6 + 56.25

Reorder the terms:
56.25 + 15q + q2 = 6 + 56.25

Combine like terms: 6 + 56.25 = 62.25
56.25 + 15q + q2 = 62.25

Factor a perfect square on the left side:
(q + 7.5)(q + 7.5) = 62.25

Calculate the square root of the right side: 7.889866919

Break this problem into two subproblems by setting 
(q + 7.5) equal to 7.889866919 and -7.889866919.

Subproblem 1
q + 7.5 = 7.889866919

Simplifying
q + 7.5 = 7.889866919

Reorder the terms:
7.5 + q = 7.889866919

Solving
7.5 + q = 7.889866919

Solving for variable 'q'.

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

Add '-7.5' to each side of the equation.
7.5 + -7.5 + q = 7.889866919 + -7.5

Combine like terms: 7.5 + -7.5 = 0.0
0.0 + q = 7.889866919 + -7.5
q = 7.889866919 + -7.5

Combine like terms: 7.889866919 + -7.5 = 0.389866919
q = 0.389866919

Simplifying
q = 0.389866919

Subproblem 2
q + 7.5 = -7.889866919

Simplifying
q + 7.5 = -7.889866919

Reorder the terms:
7.5 + q = -7.889866919

Solving
7.5 + q = -7.889866919

Solving for variable 'q'.

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

Add '-7.5' to each side of the equation.
7.5 + -7.5 + q = -7.889866919 + -7.5

Combine like terms: 7.5 + -7.5 = 0.0
0.0 + q = -7.889866919 + -7.5
q = -7.889866919 + -7.5

Combine like terms: -7.889866919 + -7.5 = -15.389866919
q = -15.389866919

Simplifying
q = -15.389866919

Solution
The solution to the problem is based on the solutions
from the subproblems.
q = {0.389866919, -15.389866919}
Solution
q = {0.389866919, -15.389866919}