-3q^2-6q+75=0

Solution for -3q^2-6q+75=0 equation:

Simplifying
-3q2 + -6q + 75 = 0

Reorder the terms:
75 + -6q + -3q2 = 0

Solving
75 + -6q + -3q2 = 0

Solving for variable 'q'.

Factor out the Greatest Common Factor (GCF), '3'.
3(25 + -2q + -1q2) = 0

Ignore the factor 3.
Subproblem 1
Set the factor '(25 + -2q + -1q2)' equal to zero and attempt to solve:

Simplifying
25 + -2q + -1q2 = 0

Solving
25 + -2q + -1q2 = 0

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

Divide each side by '-1'.
-25 + 2q + q2 = 0

Move the constant term to the right:

Add '25' to each side of the equation.
-25 + 2q + 25 + q2 = 0 + 25

Reorder the terms:
-25 + 25 + 2q + q2 = 0 + 25

Combine like terms: -25 + 25 = 0
0 + 2q + q2 = 0 + 25
2q + q2 = 0 + 25

Combine like terms: 0 + 25 = 25
2q + q2 = 25

The q term is 2q.  Take half its coefficient (1).
Square it (1) and add it to both sides.

Add '1' to each side of the equation.
2q + 1 + q2 = 25 + 1

Reorder the terms:
1 + 2q + q2 = 25 + 1

Combine like terms: 25 + 1 = 26
1 + 2q + q2 = 26

Factor a perfect square on the left side:
(q + 1)(q + 1) = 26

Calculate the square root of the right side: 5.099019514

Break this problem into two subproblems by setting 
(q + 1) equal to 5.099019514 and -5.099019514.

Subproblem 1
q + 1 = 5.099019514

Simplifying
q + 1 = 5.099019514

Reorder the terms:
1 + q = 5.099019514

Solving
1 + q = 5.099019514

Solving for variable 'q'.

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

Add '-1' to each side of the equation.
1 + -1 + q = 5.099019514 + -1

Combine like terms: 1 + -1 = 0
0 + q = 5.099019514 + -1
q = 5.099019514 + -1

Combine like terms: 5.099019514 + -1 = 4.099019514
q = 4.099019514

Simplifying
q = 4.099019514

Subproblem 2
q + 1 = -5.099019514

Simplifying
q + 1 = -5.099019514

Reorder the terms:
1 + q = -5.099019514

Solving
1 + q = -5.099019514

Solving for variable 'q'.

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

Add '-1' to each side of the equation.
1 + -1 + q = -5.099019514 + -1

Combine like terms: 1 + -1 = 0
0 + q = -5.099019514 + -1
q = -5.099019514 + -1

Combine like terms: -5.099019514 + -1 = -6.099019514
q = -6.099019514

Simplifying
q = -6.099019514

Solution
The solution to the problem is based on the solutions
from the subproblems.
q = {4.099019514, -6.099019514}
Solution
q = {4.099019514, -6.099019514}