x+2x(x+10)=12-5x

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Solution for x+2x(x+10)=12-5x equation: 


Simplifying
x + 2x(x + 10) = 12 + -5x

Reorder the terms:
x + 2x(10 + x) = 12 + -5x
x + (10 * 2x + x * 2x) = 12 + -5x
x + (20x + 2x2) = 12 + -5x

Combine like terms: x + 20x = 21x
21x + 2x2 = 12 + -5x

Solving
21x + 2x2 = 12 + -5x

Solving for variable 'x'.

Reorder the terms:
-12 + 21x + 5x + 2x2 = 12 + -5x + -12 + 5x

Combine like terms: 21x + 5x = 26x
-12 + 26x + 2x2 = 12 + -5x + -12 + 5x

Reorder the terms:
-12 + 26x + 2x2 = 12 + -12 + -5x + 5x

Combine like terms: 12 + -12 = 0
-12 + 26x + 2x2 = 0 + -5x + 5x
-12 + 26x + 2x2 = -5x + 5x

Combine like terms: -5x + 5x = 0
-12 + 26x + 2x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-6 + 13x + x2) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(-6 + 13x + x2)' equal to zero and attempt to solve:

Simplifying
-6 + 13x + x2 = 0

Solving
-6 + 13x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '6' to each side of the equation.
-6 + 13x + 6 + x2 = 0 + 6

Reorder the terms:
-6 + 6 + 13x + x2 = 0 + 6

Combine like terms: -6 + 6 = 0
0 + 13x + x2 = 0 + 6
13x + x2 = 0 + 6

Combine like terms: 0 + 6 = 6
13x + x2 = 6

The x term is 13x.  Take half its coefficient (6.5).
Square it (42.25) and add it to both sides.

Add '42.25' to each side of the equation.
13x + 42.25 + x2 = 6 + 42.25

Reorder the terms:
42.25 + 13x + x2 = 6 + 42.25

Combine like terms: 6 + 42.25 = 48.25
42.25 + 13x + x2 = 48.25

Factor a perfect square on the left side:
(x + 6.5)(x + 6.5) = 48.25

Calculate the square root of the right side: 6.946221995

Break this problem into two subproblems by setting 
(x + 6.5) equal to 6.946221995 and -6.946221995.


Subproblem 1
x + 6.5 = 6.946221995

Simplifying
x + 6.5 = 6.946221995

Reorder the terms:
6.5 + x = 6.946221995

Solving
6.5 + x = 6.946221995

Solving for variable 'x'.

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

Add '-6.5' to each side of the equation.
6.5 + -6.5 + x = 6.946221995 + -6.5

Combine like terms: 6.5 + -6.5 = 0.0
0.0 + x = 6.946221995 + -6.5
x = 6.946221995 + -6.5

Combine like terms: 6.946221995 + -6.5 = 0.446221995
x = 0.446221995

Simplifying
x = 0.446221995


Subproblem 2
x + 6.5 = -6.946221995

Simplifying
x + 6.5 = -6.946221995

Reorder the terms:
6.5 + x = -6.946221995

Solving
6.5 + x = -6.946221995

Solving for variable 'x'.

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

Add '-6.5' to each side of the equation.
6.5 + -6.5 + x = -6.946221995 + -6.5

Combine like terms: 6.5 + -6.5 = 0.0
0.0 + x = -6.946221995 + -6.5
x = -6.946221995 + -6.5

Combine like terms: -6.946221995 + -6.5 = -13.446221995
x = -13.446221995

Simplifying
x = -13.446221995


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {0.446221995, -13.446221995}
Solution
x = {0.446221995, -13.446221995}

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