-15=5q(3q-10)-5q

Solution for -15=5q(3q-10)-5q equation:

Simplifying
-15 = 5q(3q + -10) + -5q

Reorder the terms:
-15 = 5q(-10 + 3q) + -5q
-15 = (-10 * 5q + 3q * 5q) + -5q
-15 = (-50q + 15q2) + -5q

Reorder the terms:
-15 = -50q + -5q + 15q2

Combine like terms: -50q + -5q = -55q
-15 = -55q + 15q2

Solving
-15 = -55q + 15q2

Solving for variable 'q'.

Reorder the terms:
-15 + 55q + -15q2 = -55q + 55q + 15q2 + -15q2

Combine like terms: -55q + 55q = 0
-15 + 55q + -15q2 = 0 + 15q2 + -15q2
-15 + 55q + -15q2 = 15q2 + -15q2

Combine like terms: 15q2 + -15q2 = 0
-15 + 55q + -15q2 = 0

Factor out the Greatest Common Factor (GCF), '5'.
5(-3 + 11q + -3q2) = 0

Ignore the factor 5.
Subproblem 1
Set the factor '(-3 + 11q + -3q2)' equal to zero and attempt to solve:

Simplifying
-3 + 11q + -3q2 = 0

Solving
-3 + 11q + -3q2 = 0

Begin completing the square.  Divide all terms by
-3 the coefficient of the squared term: 

Divide each side by '-3'.
1 + -3.666666667q + q2 = 0

Move the constant term to the right:

Add '-1' to each side of the equation.
1 + -3.666666667q + -1 + q2 = 0 + -1

Reorder the terms:
1 + -1 + -3.666666667q + q2 = 0 + -1

Combine like terms: 1 + -1 = 0
0 + -3.666666667q + q2 = 0 + -1
-3.666666667q + q2 = 0 + -1

Combine like terms: 0 + -1 = -1
-3.666666667q + q2 = -1

The q term is -3.666666667q.  Take half its coefficient (-1.833333334).
Square it (3.361111114) and add it to both sides.

Add '3.361111114' to each side of the equation.
-3.666666667q + 3.361111114 + q2 = -1 + 3.361111114

Reorder the terms:
3.361111114 + -3.666666667q + q2 = -1 + 3.361111114

Combine like terms: -1 + 3.361111114 = 2.361111114
3.361111114 + -3.666666667q + q2 = 2.361111114

Factor a perfect square on the left side:
(q + -1.833333334)(q + -1.833333334) = 2.361111114

Calculate the square root of the right side: 1.536590744

Break this problem into two subproblems by setting 
(q + -1.833333334) equal to 1.536590744 and -1.536590744.

Subproblem 1
q + -1.833333334 = 1.536590744

Simplifying
q + -1.833333334 = 1.536590744

Reorder the terms:
-1.833333334 + q = 1.536590744

Solving
-1.833333334 + q = 1.536590744

Solving for variable 'q'.

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

Add '1.833333334' to each side of the equation.
-1.833333334 + 1.833333334 + q = 1.536590744 + 1.833333334

Combine like terms: -1.833333334 + 1.833333334 = 0.000000000
0.000000000 + q = 1.536590744 + 1.833333334
q = 1.536590744 + 1.833333334

Combine like terms: 1.536590744 + 1.833333334 = 3.369924078
q = 3.369924078

Simplifying
q = 3.369924078

Subproblem 2
q + -1.833333334 = -1.536590744

Simplifying
q + -1.833333334 = -1.536590744

Reorder the terms:
-1.833333334 + q = -1.536590744

Solving
-1.833333334 + q = -1.536590744

Solving for variable 'q'.

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

Add '1.833333334' to each side of the equation.
-1.833333334 + 1.833333334 + q = -1.536590744 + 1.833333334

Combine like terms: -1.833333334 + 1.833333334 = 0.000000000
0.000000000 + q = -1.536590744 + 1.833333334
q = -1.536590744 + 1.833333334

Combine like terms: -1.536590744 + 1.833333334 = 0.29674259
q = 0.29674259

Simplifying
q = 0.29674259

Solution
The solution to the problem is based on the solutions
from the subproblems.
q = {3.369924078, 0.29674259}
Solution
q = {3.369924078, 0.29674259}