15+12x(10-x)=141

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


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

Solving
15 + 120x + -12x2 = 141

Solving for variable 'x'.

Reorder the terms:
15 + -141 + 120x + -12x2 = 141 + -141

Combine like terms: 15 + -141 = -126
-126 + 120x + -12x2 = 141 + -141

Combine like terms: 141 + -141 = 0
-126 + 120x + -12x2 = 0

Factor out the Greatest Common Factor (GCF), '6'.
6(-21 + 20x + -2x2) = 0

Ignore the factor 6.

Subproblem 1
Set the factor '(-21 + 20x + -2x2)' equal to zero and attempt to solve:

Simplifying
-21 + 20x + -2x2 = 0

Solving
-21 + 20x + -2x2 = 0

Begin completing the square.  Divide all terms by
-2 the coefficient of the squared term: 

Divide each side by '-2'.
10.5 + -10x + x2 = 0

Move the constant term to the right:

Add '-10.5' to each side of the equation.
10.5 + -10x + -10.5 + x2 = 0 + -10.5

Reorder the terms:
10.5 + -10.5 + -10x + x2 = 0 + -10.5

Combine like terms: 10.5 + -10.5 = 0.0
0.0 + -10x + x2 = 0 + -10.5
-10x + x2 = 0 + -10.5

Combine like terms: 0 + -10.5 = -10.5
-10x + x2 = -10.5

The x term is -10x.  Take half its coefficient (-5).
Square it (25) and add it to both sides.

Add '25' to each side of the equation.
-10x + 25 + x2 = -10.5 + 25

Reorder the terms:
25 + -10x + x2 = -10.5 + 25

Combine like terms: -10.5 + 25 = 14.5
25 + -10x + x2 = 14.5

Factor a perfect square on the left side:
(x + -5)(x + -5) = 14.5

Calculate the square root of the right side: 3.807886553

Break this problem into two subproblems by setting 
(x + -5) equal to 3.807886553 and -3.807886553.


Subproblem 1
x + -5 = 3.807886553

Simplifying
x + -5 = 3.807886553

Reorder the terms:
-5 + x = 3.807886553

Solving
-5 + x = 3.807886553

Solving for variable 'x'.

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

Add '5' to each side of the equation.
-5 + 5 + x = 3.807886553 + 5

Combine like terms: -5 + 5 = 0
0 + x = 3.807886553 + 5
x = 3.807886553 + 5

Combine like terms: 3.807886553 + 5 = 8.807886553
x = 8.807886553

Simplifying
x = 8.807886553


Subproblem 2
x + -5 = -3.807886553

Simplifying
x + -5 = -3.807886553

Reorder the terms:
-5 + x = -3.807886553

Solving
-5 + x = -3.807886553

Solving for variable 'x'.

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

Add '5' to each side of the equation.
-5 + 5 + x = -3.807886553 + 5

Combine like terms: -5 + 5 = 0
0 + x = -3.807886553 + 5
x = -3.807886553 + 5

Combine like terms: -3.807886553 + 5 = 1.192113447
x = 1.192113447

Simplifying
x = 1.192113447


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {8.807886553, 1.192113447}
Solution
x = {8.807886553, 1.192113447}

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