x-2x(x+10)=12

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

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

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

Combine like terms: x + -20x = -19x
-19x + -2x2 = 12

Solving
-19x + -2x2 = 12

Solving for variable 'x'.

Reorder the terms:
-12 + -19x + -2x2 = 12 + -12

Combine like terms: 12 + -12 = 0
-12 + -19x + -2x2 = 0

Factor out the Greatest Common Factor (GCF), '-1'.
-1(12 + 19x + 2x2) = 0

Ignore the factor -1.
Subproblem 1
Set the factor '(12 + 19x + 2x2)' equal to zero and attempt to solve:

Simplifying
12 + 19x + 2x2 = 0

Solving
12 + 19x + 2x2 = 0

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

Divide each side by '2'.
6 + 9.5x + x2 = 0

Move the constant term to the right:

Add '-6' to each side of the equation.
6 + 9.5x + -6 + x2 = 0 + -6

Reorder the terms:
6 + -6 + 9.5x + x2 = 0 + -6

Combine like terms: 6 + -6 = 0
0 + 9.5x + x2 = 0 + -6
9.5x + x2 = 0 + -6

Combine like terms: 0 + -6 = -6
9.5x + x2 = -6

The x term is 9.5x.  Take half its coefficient (4.75).
Square it (22.5625) and add it to both sides.

Add '22.5625' to each side of the equation.
9.5x + 22.5625 + x2 = -6 + 22.5625

Reorder the terms:
22.5625 + 9.5x + x2 = -6 + 22.5625

Combine like terms: -6 + 22.5625 = 16.5625
22.5625 + 9.5x + x2 = 16.5625

Factor a perfect square on the left side:
(x + 4.75)(x + 4.75) = 16.5625

Calculate the square root of the right side: 4.069705149

Break this problem into two subproblems by setting 
(x + 4.75) equal to 4.069705149 and -4.069705149.

Subproblem 1
x + 4.75 = 4.069705149

Simplifying
x + 4.75 = 4.069705149

Reorder the terms:
4.75 + x = 4.069705149

Solving
4.75 + x = 4.069705149

Solving for variable 'x'.

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

Add '-4.75' to each side of the equation.
4.75 + -4.75 + x = 4.069705149 + -4.75

Combine like terms: 4.75 + -4.75 = 0.00
0.00 + x = 4.069705149 + -4.75
x = 4.069705149 + -4.75

Combine like terms: 4.069705149 + -4.75 = -0.680294851
x = -0.680294851

Simplifying
x = -0.680294851

Subproblem 2
x + 4.75 = -4.069705149

Simplifying
x + 4.75 = -4.069705149

Reorder the terms:
4.75 + x = -4.069705149

Solving
4.75 + x = -4.069705149

Solving for variable 'x'.

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

Add '-4.75' to each side of the equation.
4.75 + -4.75 + x = -4.069705149 + -4.75

Combine like terms: 4.75 + -4.75 = 0.00
0.00 + x = -4.069705149 + -4.75
x = -4.069705149 + -4.75

Combine like terms: -4.069705149 + -4.75 = -8.819705149
x = -8.819705149

Simplifying
x = -8.819705149

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {-0.680294851, -8.819705149}
Solution
x = {-0.680294851, -8.819705149}