0.2672=(12+x)(12+85+x)

Solution for 0.2672=(12+x)(12+85+x) equation:

Simplifying
0.2672 = (12 + x)(12 + 85 + x)

Combine like terms: 12 + 85 = 97
0.2672 = (12 + x)(97 + x)

Multiply (12 + x) * (97 + x)
0.2672 = (12(97 + x) + x(97 + x))
0.2672 = ((97 * 12 + x * 12) + x(97 + x))
0.2672 = ((1164 + 12x) + x(97 + x))
0.2672 = (1164 + 12x + (97 * x + x * x))
0.2672 = (1164 + 12x + (97x + x2))

Combine like terms: 12x + 97x = 109x
0.2672 = (1164 + 109x + x2)

Solving
0.2672 = 1164 + 109x + x2

Solving for variable 'x'.

Combine like terms: 0.2672 + -1164 = -1163.7328
-1163.7328 + -109x + -1x2 = 1164 + 109x + x2 + -1164 + -109x + -1x2

Reorder the terms:
-1163.7328 + -109x + -1x2 = 1164 + -1164 + 109x + -109x + x2 + -1x2

Combine like terms: 1164 + -1164 = 0
-1163.7328 + -109x + -1x2 = 0 + 109x + -109x + x2 + -1x2
-1163.7328 + -109x + -1x2 = 109x + -109x + x2 + -1x2

Combine like terms: 109x + -109x = 0
-1163.7328 + -109x + -1x2 = 0 + x2 + -1x2
-1163.7328 + -109x + -1x2 = x2 + -1x2

Combine like terms: x2 + -1x2 = 0
-1163.7328 + -109x + -1x2 = 0

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

Divide each side by '-1'.
1163.7328 + 109x + x2 = 0

Move the constant term to the right:

Add '-1163.7328' to each side of the equation.
1163.7328 + 109x + -1163.7328 + x2 = 0 + -1163.7328

Reorder the terms:
1163.7328 + -1163.7328 + 109x + x2 = 0 + -1163.7328

Combine like terms: 1163.7328 + -1163.7328 = 0.0000
0.0000 + 109x + x2 = 0 + -1163.7328
109x + x2 = 0 + -1163.7328

Combine like terms: 0 + -1163.7328 = -1163.7328
109x + x2 = -1163.7328

The x term is 109x.  Take half its coefficient (54.5).
Square it (2970.25) and add it to both sides.

Add '2970.25' to each side of the equation.
109x + 2970.25 + x2 = -1163.7328 + 2970.25

Reorder the terms:
2970.25 + 109x + x2 = -1163.7328 + 2970.25

Combine like terms: -1163.7328 + 2970.25 = 1806.5172
2970.25 + 109x + x2 = 1806.5172

Factor a perfect square on the left side:
(x + 54.5)(x + 54.5) = 1806.5172

Calculate the square root of the right side: 42.503143413

Break this problem into two subproblems by setting 
(x + 54.5) equal to 42.503143413 and -42.503143413.

Subproblem 1
x + 54.5 = 42.503143413

Simplifying
x + 54.5 = 42.503143413

Reorder the terms:
54.5 + x = 42.503143413

Solving
54.5 + x = 42.503143413

Solving for variable 'x'.

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

Add '-54.5' to each side of the equation.
54.5 + -54.5 + x = 42.503143413 + -54.5

Combine like terms: 54.5 + -54.5 = 0.0
0.0 + x = 42.503143413 + -54.5
x = 42.503143413 + -54.5

Combine like terms: 42.503143413 + -54.5 = -11.996856587
x = -11.996856587

Simplifying
x = -11.996856587

Subproblem 2
x + 54.5 = -42.503143413

Simplifying
x + 54.5 = -42.503143413

Reorder the terms:
54.5 + x = -42.503143413

Solving
54.5 + x = -42.503143413

Solving for variable 'x'.

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

Add '-54.5' to each side of the equation.
54.5 + -54.5 + x = -42.503143413 + -54.5

Combine like terms: 54.5 + -54.5 = 0.0
0.0 + x = -42.503143413 + -54.5
x = -42.503143413 + -54.5

Combine like terms: -42.503143413 + -54.5 = -97.003143413
x = -97.003143413

Simplifying
x = -97.003143413

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {-11.996856587, -97.003143413}