-7=3(q-5)q

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Solution for -7=3(q-5)q equation:


Simplifying
-7 = 3(q + -5) * q

Reorder the terms:
-7 = 3(-5 + q) * q

Reorder the terms for easier multiplication:
-7 = 3q(-5 + q)
-7 = (-5 * 3q + q * 3q)
-7 = (-15q + 3q2)

Solving
-7 = -15q + 3q2

Solving for variable 'q'.

Reorder the terms:
-7 + 15q + -3q2 = -15q + 15q + 3q2 + -3q2

Combine like terms: -15q + 15q = 0
-7 + 15q + -3q2 = 0 + 3q2 + -3q2
-7 + 15q + -3q2 = 3q2 + -3q2

Combine like terms: 3q2 + -3q2 = 0
-7 + 15q + -3q2 = 0

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

Divide each side by '-3'.
2.333333333 + -5q + q2 = 0

Move the constant term to the right:

Add '-2.333333333' to each side of the equation.
2.333333333 + -5q + -2.333333333 + q2 = 0 + -2.333333333

Reorder the terms:
2.333333333 + -2.333333333 + -5q + q2 = 0 + -2.333333333

Combine like terms: 2.333333333 + -2.333333333 = 0.000000000
0.000000000 + -5q + q2 = 0 + -2.333333333
-5q + q2 = 0 + -2.333333333

Combine like terms: 0 + -2.333333333 = -2.333333333
-5q + q2 = -2.333333333

The q term is -5q.  Take half its coefficient (-2.5).
Square it (6.25) and add it to both sides.

Add '6.25' to each side of the equation.
-5q + 6.25 + q2 = -2.333333333 + 6.25

Reorder the terms:
6.25 + -5q + q2 = -2.333333333 + 6.25

Combine like terms: -2.333333333 + 6.25 = 3.916666667
6.25 + -5q + q2 = 3.916666667

Factor a perfect square on the left side:
(q + -2.5)(q + -2.5) = 3.916666667

Calculate the square root of the right side: 1.979057015

Break this problem into two subproblems by setting 
(q + -2.5) equal to 1.979057015 and -1.979057015.


Subproblem 1
q + -2.5 = 1.979057015

Simplifying
q + -2.5 = 1.979057015

Reorder the terms:
-2.5 + q = 1.979057015

Solving
-2.5 + q = 1.979057015

Solving for variable 'q'.

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

Add '2.5' to each side of the equation.
-2.5 + 2.5 + q = 1.979057015 + 2.5

Combine like terms: -2.5 + 2.5 = 0.0
0.0 + q = 1.979057015 + 2.5
q = 1.979057015 + 2.5

Combine like terms: 1.979057015 + 2.5 = 4.479057015
q = 4.479057015

Simplifying
q = 4.479057015


Subproblem 2
q + -2.5 = -1.979057015

Simplifying
q + -2.5 = -1.979057015

Reorder the terms:
-2.5 + q = -1.979057015

Solving
-2.5 + q = -1.979057015

Solving for variable 'q'.

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

Add '2.5' to each side of the equation.
-2.5 + 2.5 + q = -1.979057015 + 2.5

Combine like terms: -2.5 + 2.5 = 0.0
0.0 + q = -1.979057015 + 2.5
q = -1.979057015 + 2.5

Combine like terms: -1.979057015 + 2.5 = 0.520942985
q = 0.520942985

Simplifying
q = 0.520942985


Solution
The solution to the problem is based on the solutions
from the subproblems.
q = {4.479057015, 0.520942985}

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