(q+6)=(q*5(q-3))

Solution for (q+6)=(q*5(q-3)) equation:

Simplifying
(q + 6) = (q * 5(q + -3))

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

Remove parenthesis around (6 + q)
6 + q = (q * 5(q + -3))

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

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

Remove parenthesis around (-15q + 5q2)
6 + q = -15q + 5q2

Solving
6 + q = -15q + 5q2

Solving for variable 'q'.

Combine like terms: q + 15q = 16q
6 + 16q + -5q2 = -15q + 5q2 + 15q + -5q2

Reorder the terms:
6 + 16q + -5q2 = -15q + 15q + 5q2 + -5q2

Combine like terms: -15q + 15q = 0
6 + 16q + -5q2 = 0 + 5q2 + -5q2
6 + 16q + -5q2 = 5q2 + -5q2

Combine like terms: 5q2 + -5q2 = 0
6 + 16q + -5q2 = 0

Begin completing the square.  Divide all terms by
-5 the coefficient of the squared term: 

Divide each side by '-5'.
-1.2 + -3.2q + q2 = 0

Move the constant term to the right:

Add '1.2' to each side of the equation.
-1.2 + -3.2q + 1.2 + q2 = 0 + 1.2

Reorder the terms:
-1.2 + 1.2 + -3.2q + q2 = 0 + 1.2

Combine like terms: -1.2 + 1.2 = 0.0
0.0 + -3.2q + q2 = 0 + 1.2
-3.2q + q2 = 0 + 1.2

Combine like terms: 0 + 1.2 = 1.2
-3.2q + q2 = 1.2

The q term is -3.2q.  Take half its coefficient (-1.6).
Square it (2.56) and add it to both sides.

Add '2.56' to each side of the equation.
-3.2q + 2.56 + q2 = 1.2 + 2.56

Reorder the terms:
2.56 + -3.2q + q2 = 1.2 + 2.56

Combine like terms: 1.2 + 2.56 = 3.76
2.56 + -3.2q + q2 = 3.76

Factor a perfect square on the left side:
(q + -1.6)(q + -1.6) = 3.76

Calculate the square root of the right side: 1.939071943

Break this problem into two subproblems by setting 
(q + -1.6) equal to 1.939071943 and -1.939071943.

Subproblem 1
q + -1.6 = 1.939071943

Simplifying
q + -1.6 = 1.939071943

Reorder the terms:
-1.6 + q = 1.939071943

Solving
-1.6 + q = 1.939071943

Solving for variable 'q'.

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

Add '1.6' to each side of the equation.
-1.6 + 1.6 + q = 1.939071943 + 1.6

Combine like terms: -1.6 + 1.6 = 0.0
0.0 + q = 1.939071943 + 1.6
q = 1.939071943 + 1.6

Combine like terms: 1.939071943 + 1.6 = 3.539071943
q = 3.539071943

Simplifying
q = 3.539071943

Subproblem 2
q + -1.6 = -1.939071943

Simplifying
q + -1.6 = -1.939071943

Reorder the terms:
-1.6 + q = -1.939071943

Solving
-1.6 + q = -1.939071943

Solving for variable 'q'.

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

Add '1.6' to each side of the equation.
-1.6 + 1.6 + q = -1.939071943 + 1.6

Combine like terms: -1.6 + 1.6 = 0.0
0.0 + q = -1.939071943 + 1.6
q = -1.939071943 + 1.6

Combine like terms: -1.939071943 + 1.6 = -0.339071943
q = -0.339071943

Simplifying
q = -0.339071943

Solution
The solution to the problem is based on the solutions
from the subproblems.
q = {3.539071943, -0.339071943}