12+6q(5-q)=

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Solution for 12+6q(5-q)= equation: 


Simplifying
12 + 6q(5 + -1q) = 0
12 + (5 * 6q + -1q * 6q) = 0
12 + (30q + -6q2) = 0

Solving
12 + 30q + -6q2 = 0

Solving for variable 'q'.

Factor out the Greatest Common Factor (GCF), '6'.
6(2 + 5q + -1q2) = 0

Ignore the factor 6.

Subproblem 1
Set the factor '(2 + 5q + -1q2)' equal to zero and attempt to solve:

Simplifying
2 + 5q + -1q2 = 0

Solving
2 + 5q + -1q2 = 0

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

Divide each side by '-1'.
-2 + -5q + q2 = 0

Move the constant term to the right:

Add '2' to each side of the equation.
-2 + -5q + 2 + q2 = 0 + 2

Reorder the terms:
-2 + 2 + -5q + q2 = 0 + 2

Combine like terms: -2 + 2 = 0
0 + -5q + q2 = 0 + 2
-5q + q2 = 0 + 2

Combine like terms: 0 + 2 = 2
-5q + q2 = 2

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 + 6.25

Reorder the terms:
6.25 + -5q + q2 = 2 + 6.25

Combine like terms: 2 + 6.25 = 8.25
6.25 + -5q + q2 = 8.25

Factor a perfect square on the left side:
(q + -2.5)(q + -2.5) = 8.25

Calculate the square root of the right side: 2.872281323

Break this problem into two subproblems by setting 
(q + -2.5) equal to 2.872281323 and -2.872281323.


Subproblem 1
q + -2.5 = 2.872281323

Simplifying
q + -2.5 = 2.872281323

Reorder the terms:
-2.5 + q = 2.872281323

Solving
-2.5 + q = 2.872281323

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 = 2.872281323 + 2.5

Combine like terms: -2.5 + 2.5 = 0.0
0.0 + q = 2.872281323 + 2.5
q = 2.872281323 + 2.5

Combine like terms: 2.872281323 + 2.5 = 5.372281323
q = 5.372281323

Simplifying
q = 5.372281323


Subproblem 2
q + -2.5 = -2.872281323

Simplifying
q + -2.5 = -2.872281323

Reorder the terms:
-2.5 + q = -2.872281323

Solving
-2.5 + q = -2.872281323

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 = -2.872281323 + 2.5

Combine like terms: -2.5 + 2.5 = 0.0
0.0 + q = -2.872281323 + 2.5
q = -2.872281323 + 2.5

Combine like terms: -2.872281323 + 2.5 = -0.372281323
q = -0.372281323

Simplifying
q = -0.372281323


Solution
The solution to the problem is based on the solutions
from the subproblems.
q = {5.372281323, -0.372281323}
Solution
q = {5.372281323, -0.372281323}

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