-6x(x-2)+4(3-x)=-36

Solution for -6x(x-2)+4(3-x)=-36 equation:

Simplifying
-6x(x + -2) + 4(3 + -1x) = -36

Reorder the terms:
-6x(-2 + x) + 4(3 + -1x) = -36
(-2 * -6x + x * -6x) + 4(3 + -1x) = -36
(12x + -6x2) + 4(3 + -1x) = -36
12x + -6x2 + (3 * 4 + -1x * 4) = -36
12x + -6x2 + (12 + -4x) = -36

Reorder the terms:
12 + 12x + -4x + -6x2 = -36

Combine like terms: 12x + -4x = 8x
12 + 8x + -6x2 = -36

Solving
12 + 8x + -6x2 = -36

Solving for variable 'x'.

Reorder the terms:
12 + 36 + 8x + -6x2 = -36 + 36

Combine like terms: 12 + 36 = 48
48 + 8x + -6x2 = -36 + 36

Combine like terms: -36 + 36 = 0
48 + 8x + -6x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(24 + 4x + -3x2) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(24 + 4x + -3x2)' equal to zero and attempt to solve:

Simplifying
24 + 4x + -3x2 = 0

Solving
24 + 4x + -3x2 = 0

Begin completing the square.  Divide all terms by
-3 the coefficient of the squared term: 

Divide each side by '-3'.
-8 + -1.333333333x + x2 = 0

Move the constant term to the right:

Add '8' to each side of the equation.
-8 + -1.333333333x + 8 + x2 = 0 + 8

Reorder the terms:
-8 + 8 + -1.333333333x + x2 = 0 + 8

Combine like terms: -8 + 8 = 0
0 + -1.333333333x + x2 = 0 + 8
-1.333333333x + x2 = 0 + 8

Combine like terms: 0 + 8 = 8
-1.333333333x + x2 = 8

The x term is -1.333333333x.  Take half its coefficient (-0.6666666665).
Square it (0.4444444442) and add it to both sides.

Add '0.4444444442' to each side of the equation.
-1.333333333x + 0.4444444442 + x2 = 8 + 0.4444444442

Reorder the terms:
0.4444444442 + -1.333333333x + x2 = 8 + 0.4444444442

Combine like terms: 8 + 0.4444444442 = 8.4444444442
0.4444444442 + -1.333333333x + x2 = 8.4444444442

Factor a perfect square on the left side:
(x + -0.6666666665)(x + -0.6666666665) = 8.4444444442

Calculate the square root of the right side: 2.905932629

Break this problem into two subproblems by setting 
(x + -0.6666666665) equal to 2.905932629 and -2.905932629.

Subproblem 1
x + -0.6666666665 = 2.905932629

Simplifying
x + -0.6666666665 = 2.905932629

Reorder the terms:
-0.6666666665 + x = 2.905932629

Solving
-0.6666666665 + x = 2.905932629

Solving for variable 'x'.

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

Add '0.6666666665' to each side of the equation.
-0.6666666665 + 0.6666666665 + x = 2.905932629 + 0.6666666665

Combine like terms: -0.6666666665 + 0.6666666665 = 0.0000000000
0.0000000000 + x = 2.905932629 + 0.6666666665
x = 2.905932629 + 0.6666666665

Combine like terms: 2.905932629 + 0.6666666665 = 3.5725992955
x = 3.5725992955

Simplifying
x = 3.5725992955

Subproblem 2
x + -0.6666666665 = -2.905932629

Simplifying
x + -0.6666666665 = -2.905932629

Reorder the terms:
-0.6666666665 + x = -2.905932629

Solving
-0.6666666665 + x = -2.905932629

Solving for variable 'x'.

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

Add '0.6666666665' to each side of the equation.
-0.6666666665 + 0.6666666665 + x = -2.905932629 + 0.6666666665

Combine like terms: -0.6666666665 + 0.6666666665 = 0.0000000000
0.0000000000 + x = -2.905932629 + 0.6666666665
x = -2.905932629 + 0.6666666665

Combine like terms: -2.905932629 + 0.6666666665 = -2.2392659625
x = -2.2392659625

Simplifying
x = -2.2392659625

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {3.5725992955, -2.2392659625}
Solution
x = {3.5725992955, -2.2392659625}