10x+(12-x)=10x(12-x)+x+54

Solution for 10x+(12-x)=10x(12-x)+x+54 equation:

Simplifying
10x + (12 + -1x) = 10x(12 + -1x) + x + 54

Remove parenthesis around (12 + -1x)
10x + 12 + -1x = 10x(12 + -1x) + x + 54

Reorder the terms:
12 + 10x + -1x = 10x(12 + -1x) + x + 54

Combine like terms: 10x + -1x = 9x
12 + 9x = 10x(12 + -1x) + x + 54
12 + 9x = (12 * 10x + -1x * 10x) + x + 54
12 + 9x = (120x + -10x2) + x + 54

Reorder the terms:
12 + 9x = 54 + 120x + x + -10x2

Combine like terms: 120x + x = 121x
12 + 9x = 54 + 121x + -10x2

Solving
12 + 9x = 54 + 121x + -10x2

Solving for variable 'x'.

Reorder the terms:
12 + -54 + 9x + -121x + 10x2 = 54 + 121x + -10x2 + -54 + -121x + 10x2

Combine like terms: 12 + -54 = -42
-42 + 9x + -121x + 10x2 = 54 + 121x + -10x2 + -54 + -121x + 10x2

Combine like terms: 9x + -121x = -112x
-42 + -112x + 10x2 = 54 + 121x + -10x2 + -54 + -121x + 10x2

Reorder the terms:
-42 + -112x + 10x2 = 54 + -54 + 121x + -121x + -10x2 + 10x2

Combine like terms: 54 + -54 = 0
-42 + -112x + 10x2 = 0 + 121x + -121x + -10x2 + 10x2
-42 + -112x + 10x2 = 121x + -121x + -10x2 + 10x2

Combine like terms: 121x + -121x = 0
-42 + -112x + 10x2 = 0 + -10x2 + 10x2
-42 + -112x + 10x2 = -10x2 + 10x2

Combine like terms: -10x2 + 10x2 = 0
-42 + -112x + 10x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-21 + -56x + 5x2) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(-21 + -56x + 5x2)' equal to zero and attempt to solve:

Simplifying
-21 + -56x + 5x2 = 0

Solving
-21 + -56x + 5x2 = 0

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

Divide each side by '5'.
-4.2 + -11.2x + x2 = 0

Move the constant term to the right:

Add '4.2' to each side of the equation.
-4.2 + -11.2x + 4.2 + x2 = 0 + 4.2

Reorder the terms:
-4.2 + 4.2 + -11.2x + x2 = 0 + 4.2

Combine like terms: -4.2 + 4.2 = 0.0
0.0 + -11.2x + x2 = 0 + 4.2
-11.2x + x2 = 0 + 4.2

Combine like terms: 0 + 4.2 = 4.2
-11.2x + x2 = 4.2

The x term is -11.2x.  Take half its coefficient (-5.6).
Square it (31.36) and add it to both sides.

Add '31.36' to each side of the equation.
-11.2x + 31.36 + x2 = 4.2 + 31.36

Reorder the terms:
31.36 + -11.2x + x2 = 4.2 + 31.36

Combine like terms: 4.2 + 31.36 = 35.56
31.36 + -11.2x + x2 = 35.56

Factor a perfect square on the left side:
(x + -5.6)(x + -5.6) = 35.56

Calculate the square root of the right side: 5.963220606

Break this problem into two subproblems by setting 
(x + -5.6) equal to 5.963220606 and -5.963220606.

Subproblem 1
x + -5.6 = 5.963220606

Simplifying
x + -5.6 = 5.963220606

Reorder the terms:
-5.6 + x = 5.963220606

Solving
-5.6 + x = 5.963220606

Solving for variable 'x'.

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

Add '5.6' to each side of the equation.
-5.6 + 5.6 + x = 5.963220606 + 5.6

Combine like terms: -5.6 + 5.6 = 0.0
0.0 + x = 5.963220606 + 5.6
x = 5.963220606 + 5.6

Combine like terms: 5.963220606 + 5.6 = 11.563220606
x = 11.563220606

Simplifying
x = 11.563220606

Subproblem 2
x + -5.6 = -5.963220606

Simplifying
x + -5.6 = -5.963220606

Reorder the terms:
-5.6 + x = -5.963220606

Solving
-5.6 + x = -5.963220606

Solving for variable 'x'.

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

Add '5.6' to each side of the equation.
-5.6 + 5.6 + x = -5.963220606 + 5.6

Combine like terms: -5.6 + 5.6 = 0.0
0.0 + x = -5.963220606 + 5.6
x = -5.963220606 + 5.6

Combine like terms: -5.963220606 + 5.6 = -0.363220606
x = -0.363220606

Simplifying
x = -0.363220606

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {11.563220606, -0.363220606}
Solution
x = {11.563220606, -0.363220606}