-3q^2+6q=-123

Solution for -3q^2+6q=-123 equation:

Simplifying
-3q2 + 6q = -123

Reorder the terms:
6q + -3q2 = -123

Solving
6q + -3q2 = -123

Solving for variable 'q'.

Reorder the terms:
123 + 6q + -3q2 = -123 + 123

Combine like terms: -123 + 123 = 0
123 + 6q + -3q2 = 0

Factor out the Greatest Common Factor (GCF), '3'.
3(41 + 2q + -1q2) = 0

Ignore the factor 3.
Subproblem 1
Set the factor '(41 + 2q + -1q2)' equal to zero and attempt to solve:

Simplifying
41 + 2q + -1q2 = 0

Solving
41 + 2q + -1q2 = 0

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

Divide each side by '-1'.
-41 + -2q + q2 = 0

Move the constant term to the right:

Add '41' to each side of the equation.
-41 + -2q + 41 + q2 = 0 + 41

Reorder the terms:
-41 + 41 + -2q + q2 = 0 + 41

Combine like terms: -41 + 41 = 0
0 + -2q + q2 = 0 + 41
-2q + q2 = 0 + 41

Combine like terms: 0 + 41 = 41
-2q + q2 = 41

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 = 41 + 1

Reorder the terms:
1 + -2q + q2 = 41 + 1

Combine like terms: 41 + 1 = 42
1 + -2q + q2 = 42

Factor a perfect square on the left side:
(q + -1)(q + -1) = 42

Calculate the square root of the right side: 6.480740698

Break this problem into two subproblems by setting 
(q + -1) equal to 6.480740698 and -6.480740698.

Subproblem 1
q + -1 = 6.480740698

Simplifying
q + -1 = 6.480740698

Reorder the terms:
-1 + q = 6.480740698

Solving
-1 + q = 6.480740698

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 = 6.480740698 + 1

Combine like terms: -1 + 1 = 0
0 + q = 6.480740698 + 1
q = 6.480740698 + 1

Combine like terms: 6.480740698 + 1 = 7.480740698
q = 7.480740698

Simplifying
q = 7.480740698

Subproblem 2
q + -1 = -6.480740698

Simplifying
q + -1 = -6.480740698

Reorder the terms:
-1 + q = -6.480740698

Solving
-1 + q = -6.480740698

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 = -6.480740698 + 1

Combine like terms: -1 + 1 = 0
0 + q = -6.480740698 + 1
q = -6.480740698 + 1

Combine like terms: -6.480740698 + 1 = -5.480740698
q = -5.480740698

Simplifying
q = -5.480740698

Solution
The solution to the problem is based on the solutions
from the subproblems.
q = {7.480740698, -5.480740698}
Solution
q = {7.480740698, -5.480740698}