3q(q-4)=9

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Solution for 3q(q-4)=9 equation: 


Simplifying
3q(q + -4) = 9

Reorder the terms:
3q(-4 + q) = 9
(-4 * 3q + q * 3q) = 9
(-12q + 3q2) = 9

Solving
-12q + 3q2 = 9

Solving for variable 'q'.

Reorder the terms:
-9 + -12q + 3q2 = 9 + -9

Combine like terms: 9 + -9 = 0
-9 + -12q + 3q2 = 0

Factor out the Greatest Common Factor (GCF), '3'.
3(-3 + -4q + q2) = 0

Ignore the factor 3.

Subproblem 1
Set the factor '(-3 + -4q + q2)' equal to zero and attempt to solve:

Simplifying
-3 + -4q + q2 = 0

Solving
-3 + -4q + q2 = 0

Begin completing the square.

Move the constant term to the right:

Add '3' to each side of the equation.
-3 + -4q + 3 + q2 = 0 + 3

Reorder the terms:
-3 + 3 + -4q + q2 = 0 + 3

Combine like terms: -3 + 3 = 0
0 + -4q + q2 = 0 + 3
-4q + q2 = 0 + 3

Combine like terms: 0 + 3 = 3
-4q + q2 = 3

The q term is -4q.  Take half its coefficient (-2).
Square it (4) and add it to both sides.

Add '4' to each side of the equation.
-4q + 4 + q2 = 3 + 4

Reorder the terms:
4 + -4q + q2 = 3 + 4

Combine like terms: 3 + 4 = 7
4 + -4q + q2 = 7

Factor a perfect square on the left side:
(q + -2)(q + -2) = 7

Calculate the square root of the right side: 2.645751311

Break this problem into two subproblems by setting 
(q + -2) equal to 2.645751311 and -2.645751311.


Subproblem 1
q + -2 = 2.645751311

Simplifying
q + -2 = 2.645751311

Reorder the terms:
-2 + q = 2.645751311

Solving
-2 + q = 2.645751311

Solving for variable 'q'.

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

Add '2' to each side of the equation.
-2 + 2 + q = 2.645751311 + 2

Combine like terms: -2 + 2 = 0
0 + q = 2.645751311 + 2
q = 2.645751311 + 2

Combine like terms: 2.645751311 + 2 = 4.645751311
q = 4.645751311

Simplifying
q = 4.645751311


Subproblem 2
q + -2 = -2.645751311

Simplifying
q + -2 = -2.645751311

Reorder the terms:
-2 + q = -2.645751311

Solving
-2 + q = -2.645751311

Solving for variable 'q'.

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

Add '2' to each side of the equation.
-2 + 2 + q = -2.645751311 + 2

Combine like terms: -2 + 2 = 0
0 + q = -2.645751311 + 2
q = -2.645751311 + 2

Combine like terms: -2.645751311 + 2 = -0.645751311
q = -0.645751311

Simplifying
q = -0.645751311


Solution
The solution to the problem is based on the solutions
from the subproblems.
q = {4.645751311, -0.645751311}
Solution
q = {4.645751311, -0.645751311}

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