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

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

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

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

Reorder the terms for easier multiplication:
-15 = 5 * 5q(-10 + 3q)

Multiply 5 * 5
-15 = 25q(-10 + 3q)
-15 = (-10 * 25q + 3q * 25q)
-15 = (-250q + 75q2)

Solving
-15 = -250q + 75q2

Solving for variable 'q'.

Reorder the terms:
-15 + 250q + -75q2 = -250q + 250q + 75q2 + -75q2

Combine like terms: -250q + 250q = 0
-15 + 250q + -75q2 = 0 + 75q2 + -75q2
-15 + 250q + -75q2 = 75q2 + -75q2

Combine like terms: 75q2 + -75q2 = 0
-15 + 250q + -75q2 = 0

Factor out the Greatest Common Factor (GCF), '5'.
5(-3 + 50q + -15q2) = 0

Ignore the factor 5.
Subproblem 1
Set the factor '(-3 + 50q + -15q2)' equal to zero and attempt to solve:

Simplifying
-3 + 50q + -15q2 = 0

Solving
-3 + 50q + -15q2 = 0

Begin completing the square.  Divide all terms by
-15 the coefficient of the squared term: 

Divide each side by '-15'.
0.2 + -3.333333333q + q2 = 0

Move the constant term to the right:

Add '-0.2' to each side of the equation.
0.2 + -3.333333333q + -0.2 + q2 = 0 + -0.2

Reorder the terms:
0.2 + -0.2 + -3.333333333q + q2 = 0 + -0.2

Combine like terms: 0.2 + -0.2 = 0.0
0.0 + -3.333333333q + q2 = 0 + -0.2
-3.333333333q + q2 = 0 + -0.2

Combine like terms: 0 + -0.2 = -0.2
-3.333333333q + q2 = -0.2

The q term is -3.333333333q.  Take half its coefficient (-1.666666667).
Square it (2.777777779) and add it to both sides.

Add '2.777777779' to each side of the equation.
-3.333333333q + 2.777777779 + q2 = -0.2 + 2.777777779

Reorder the terms:
2.777777779 + -3.333333333q + q2 = -0.2 + 2.777777779

Combine like terms: -0.2 + 2.777777779 = 2.577777779
2.777777779 + -3.333333333q + q2 = 2.577777779

Factor a perfect square on the left side:
(q + -1.666666667)(q + -1.666666667) = 2.577777779

Calculate the square root of the right side: 1.605545944

Break this problem into two subproblems by setting 
(q + -1.666666667) equal to 1.605545944 and -1.605545944.

Subproblem 1
q + -1.666666667 = 1.605545944

Simplifying
q + -1.666666667 = 1.605545944

Reorder the terms:
-1.666666667 + q = 1.605545944

Solving
-1.666666667 + q = 1.605545944

Solving for variable 'q'.

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

Add '1.666666667' to each side of the equation.
-1.666666667 + 1.666666667 + q = 1.605545944 + 1.666666667

Combine like terms: -1.666666667 + 1.666666667 = 0.000000000
0.000000000 + q = 1.605545944 + 1.666666667
q = 1.605545944 + 1.666666667

Combine like terms: 1.605545944 + 1.666666667 = 3.272212611
q = 3.272212611

Simplifying
q = 3.272212611

Subproblem 2
q + -1.666666667 = -1.605545944

Simplifying
q + -1.666666667 = -1.605545944

Reorder the terms:
-1.666666667 + q = -1.605545944

Solving
-1.666666667 + q = -1.605545944

Solving for variable 'q'.

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

Add '1.666666667' to each side of the equation.
-1.666666667 + 1.666666667 + q = -1.605545944 + 1.666666667

Combine like terms: -1.666666667 + 1.666666667 = 0.000000000
0.000000000 + q = -1.605545944 + 1.666666667
q = -1.605545944 + 1.666666667

Combine like terms: -1.605545944 + 1.666666667 = 0.061120723
q = 0.061120723

Simplifying
q = 0.061120723

Solution
The solution to the problem is based on the solutions
from the subproblems.
q = {3.272212611, 0.061120723}
Solution
q = {3.272212611, 0.061120723}