3q(q-7)=27

Solution for 3q(q-7)=27 equation:

Simplifying
3q(q + -7) = 27

Reorder the terms:
3q(-7 + q) = 27
(-7 * 3q + q * 3q) = 27
(-21q + 3q2) = 27

Solving
-21q + 3q2 = 27

Solving for variable 'q'.

Reorder the terms:
-27 + -21q + 3q2 = 27 + -27

Combine like terms: 27 + -27 = 0
-27 + -21q + 3q2 = 0

Factor out the Greatest Common Factor (GCF), '3'.
3(-9 + -7q + q2) = 0

Ignore the factor 3.
Subproblem 1
Set the factor '(-9 + -7q + q2)' equal to zero and attempt to solve:

Simplifying
-9 + -7q + q2 = 0

Solving
-9 + -7q + q2 = 0

Begin completing the square.

Move the constant term to the right:

Add '9' to each side of the equation.
-9 + -7q + 9 + q2 = 0 + 9

Reorder the terms:
-9 + 9 + -7q + q2 = 0 + 9

Combine like terms: -9 + 9 = 0
0 + -7q + q2 = 0 + 9
-7q + q2 = 0 + 9

Combine like terms: 0 + 9 = 9
-7q + q2 = 9

The q term is -7q.  Take half its coefficient (-3.5).
Square it (12.25) and add it to both sides.

Add '12.25' to each side of the equation.
-7q + 12.25 + q2 = 9 + 12.25

Reorder the terms:
12.25 + -7q + q2 = 9 + 12.25

Combine like terms: 9 + 12.25 = 21.25
12.25 + -7q + q2 = 21.25

Factor a perfect square on the left side:
(q + -3.5)(q + -3.5) = 21.25

Calculate the square root of the right side: 4.609772229

Break this problem into two subproblems by setting 
(q + -3.5) equal to 4.609772229 and -4.609772229.

Subproblem 1
q + -3.5 = 4.609772229

Simplifying
q + -3.5 = 4.609772229

Reorder the terms:
-3.5 + q = 4.609772229

Solving
-3.5 + q = 4.609772229

Solving for variable 'q'.

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

Add '3.5' to each side of the equation.
-3.5 + 3.5 + q = 4.609772229 + 3.5

Combine like terms: -3.5 + 3.5 = 0.0
0.0 + q = 4.609772229 + 3.5
q = 4.609772229 + 3.5

Combine like terms: 4.609772229 + 3.5 = 8.109772229
q = 8.109772229

Simplifying
q = 8.109772229

Subproblem 2
q + -3.5 = -4.609772229

Simplifying
q + -3.5 = -4.609772229

Reorder the terms:
-3.5 + q = -4.609772229

Solving
-3.5 + q = -4.609772229

Solving for variable 'q'.

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

Add '3.5' to each side of the equation.
-3.5 + 3.5 + q = -4.609772229 + 3.5

Combine like terms: -3.5 + 3.5 = 0.0
0.0 + q = -4.609772229 + 3.5
q = -4.609772229 + 3.5

Combine like terms: -4.609772229 + 3.5 = -1.109772229
q = -1.109772229

Simplifying
q = -1.109772229

Solution
The solution to the problem is based on the solutions
from the subproblems.
q = {8.109772229, -1.109772229}
Solution
q = {8.109772229, -1.109772229}