0.96=(13+q)(14+q)

Solution for 0.96=(13+q)(14+q) equation:

Simplifying
0.96 = (13 + q)(14 + q)

Multiply (13 + q) * (14 + q)
0.96 = (13(14 + q) + q(14 + q))
0.96 = ((14 * 13 + q * 13) + q(14 + q))
0.96 = ((182 + 13q) + q(14 + q))
0.96 = (182 + 13q + (14 * q + q * q))
0.96 = (182 + 13q + (14q + q2))

Combine like terms: 13q + 14q = 27q
0.96 = (182 + 27q + q2)

Solving
0.96 = 182 + 27q + q2

Solving for variable 'q'.

Combine like terms: 0.96 + -182 = -181.04
-181.04 + -27q + -1q2 = 182 + 27q + q2 + -182 + -27q + -1q2

Reorder the terms:
-181.04 + -27q + -1q2 = 182 + -182 + 27q + -27q + q2 + -1q2

Combine like terms: 182 + -182 = 0
-181.04 + -27q + -1q2 = 0 + 27q + -27q + q2 + -1q2
-181.04 + -27q + -1q2 = 27q + -27q + q2 + -1q2

Combine like terms: 27q + -27q = 0
-181.04 + -27q + -1q2 = 0 + q2 + -1q2
-181.04 + -27q + -1q2 = q2 + -1q2

Combine like terms: q2 + -1q2 = 0
-181.04 + -27q + -1q2 = 0

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

Divide each side by '-1'.
181.04 + 27q + q2 = 0

Move the constant term to the right:

Add '-181.04' to each side of the equation.
181.04 + 27q + -181.04 + q2 = 0 + -181.04

Reorder the terms:
181.04 + -181.04 + 27q + q2 = 0 + -181.04

Combine like terms: 181.04 + -181.04 = 0.00
0.00 + 27q + q2 = 0 + -181.04
27q + q2 = 0 + -181.04

Combine like terms: 0 + -181.04 = -181.04
27q + q2 = -181.04

The q term is 27q.  Take half its coefficient (13.5).
Square it (182.25) and add it to both sides.

Add '182.25' to each side of the equation.
27q + 182.25 + q2 = -181.04 + 182.25

Reorder the terms:
182.25 + 27q + q2 = -181.04 + 182.25

Combine like terms: -181.04 + 182.25 = 1.21
182.25 + 27q + q2 = 1.21

Factor a perfect square on the left side:
(q + 13.5)(q + 13.5) = 1.21

Calculate the square root of the right side: 1.1

Break this problem into two subproblems by setting 
(q + 13.5) equal to 1.1 and -1.1.

Subproblem 1
q + 13.5 = 1.1

Simplifying
q + 13.5 = 1.1

Reorder the terms:
13.5 + q = 1.1

Solving
13.5 + q = 1.1

Solving for variable 'q'.

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

Add '-13.5' to each side of the equation.
13.5 + -13.5 + q = 1.1 + -13.5

Combine like terms: 13.5 + -13.5 = 0.0
0.0 + q = 1.1 + -13.5
q = 1.1 + -13.5

Combine like terms: 1.1 + -13.5 = -12.4
q = -12.4

Simplifying
q = -12.4

Subproblem 2
q + 13.5 = -1.1

Simplifying
q + 13.5 = -1.1

Reorder the terms:
13.5 + q = -1.1

Solving
13.5 + q = -1.1

Solving for variable 'q'.

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

Add '-13.5' to each side of the equation.
13.5 + -13.5 + q = -1.1 + -13.5

Combine like terms: 13.5 + -13.5 = 0.0
0.0 + q = -1.1 + -13.5
q = -1.1 + -13.5

Combine like terms: -1.1 + -13.5 = -14.6
q = -14.6

Simplifying
q = -14.6

Solution
The solution to the problem is based on the solutions
from the subproblems.
q = {-12.4, -14.6}