15x+12x(10-x)=141

Solution for 15x+12x(10-x)=141 equation:

Simplifying
15x + 12x(10 + -1x) = 141
15x + (10 * 12x + -1x * 12x) = 141
15x + (120x + -12x2) = 141

Combine like terms: 15x + 120x = 135x
135x + -12x2 = 141

Solving
135x + -12x2 = 141

Solving for variable 'x'.

Reorder the terms:
-141 + 135x + -12x2 = 141 + -141

Combine like terms: 141 + -141 = 0
-141 + 135x + -12x2 = 0

Factor out the Greatest Common Factor (GCF), '3'.
3(-47 + 45x + -4x2) = 0

Ignore the factor 3.
Subproblem 1
Set the factor '(-47 + 45x + -4x2)' equal to zero and attempt to solve:

Simplifying
-47 + 45x + -4x2 = 0

Solving
-47 + 45x + -4x2 = 0

Begin completing the square.  Divide all terms by
-4 the coefficient of the squared term: 

Divide each side by '-4'.
11.75 + -11.25x + x2 = 0

Move the constant term to the right:

Add '-11.75' to each side of the equation.
11.75 + -11.25x + -11.75 + x2 = 0 + -11.75

Reorder the terms:
11.75 + -11.75 + -11.25x + x2 = 0 + -11.75

Combine like terms: 11.75 + -11.75 = 0.00
0.00 + -11.25x + x2 = 0 + -11.75
-11.25x + x2 = 0 + -11.75

Combine like terms: 0 + -11.75 = -11.75
-11.25x + x2 = -11.75

The x term is -11.25x.  Take half its coefficient (-5.625).
Square it (31.640625) and add it to both sides.

Add '31.640625' to each side of the equation.
-11.25x + 31.640625 + x2 = -11.75 + 31.640625

Reorder the terms:
31.640625 + -11.25x + x2 = -11.75 + 31.640625

Combine like terms: -11.75 + 31.640625 = 19.890625
31.640625 + -11.25x + x2 = 19.890625

Factor a perfect square on the left side:
(x + -5.625)(x + -5.625) = 19.890625

Calculate the square root of the right side: 4.459890694

Break this problem into two subproblems by setting 
(x + -5.625) equal to 4.459890694 and -4.459890694.

Subproblem 1
x + -5.625 = 4.459890694

Simplifying
x + -5.625 = 4.459890694

Reorder the terms:
-5.625 + x = 4.459890694

Solving
-5.625 + x = 4.459890694

Solving for variable 'x'.

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

Add '5.625' to each side of the equation.
-5.625 + 5.625 + x = 4.459890694 + 5.625

Combine like terms: -5.625 + 5.625 = 0.000
0.000 + x = 4.459890694 + 5.625
x = 4.459890694 + 5.625

Combine like terms: 4.459890694 + 5.625 = 10.084890694
x = 10.084890694

Simplifying
x = 10.084890694

Subproblem 2
x + -5.625 = -4.459890694

Simplifying
x + -5.625 = -4.459890694

Reorder the terms:
-5.625 + x = -4.459890694

Solving
-5.625 + x = -4.459890694

Solving for variable 'x'.

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

Add '5.625' to each side of the equation.
-5.625 + 5.625 + x = -4.459890694 + 5.625

Combine like terms: -5.625 + 5.625 = 0.000
0.000 + x = -4.459890694 + 5.625
x = -4.459890694 + 5.625

Combine like terms: -4.459890694 + 5.625 = 1.165109306
x = 1.165109306

Simplifying
x = 1.165109306

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {10.084890694, 1.165109306}
Solution
x = {10.084890694, 1.165109306}