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

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

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

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

Reorder the terms for easier multiplication:
-6 * 4(-2 + x)(3 + -6x) = -36

Multiply -6 * 4
-24(-2 + x)(3 + -6x) = -36

Multiply (-2 + x) * (3 + -6x)
-24(-2(3 + -6x) + x(3 + -6x)) = -36
-24((3 * -2 + -6x * -2) + x(3 + -6x)) = -36
-24((-6 + 12x) + x(3 + -6x)) = -36
-24(-6 + 12x + (3 * x + -6x * x)) = -36
-24(-6 + 12x + (3x + -6x2)) = -36

Combine like terms: 12x + 3x = 15x
-24(-6 + 15x + -6x2) = -36
(-6 * -24 + 15x * -24 + -6x2 * -24) = -36
(144 + -360x + 144x2) = -36

Solving
144 + -360x + 144x2 = -36

Solving for variable 'x'.

Reorder the terms:
144 + 36 + -360x + 144x2 = -36 + 36

Combine like terms: 144 + 36 = 180
180 + -360x + 144x2 = -36 + 36

Combine like terms: -36 + 36 = 0
180 + -360x + 144x2 = 0

Factor out the Greatest Common Factor (GCF), '36'.
36(5 + -10x + 4x2) = 0

Ignore the factor 36.
Subproblem 1
Set the factor '(5 + -10x + 4x2)' equal to zero and attempt to solve:

Simplifying
5 + -10x + 4x2 = 0

Solving
5 + -10x + 4x2 = 0

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

Divide each side by '4'.
1.25 + -2.5x + x2 = 0

Move the constant term to the right:

Add '-1.25' to each side of the equation.
1.25 + -2.5x + -1.25 + x2 = 0 + -1.25

Reorder the terms:
1.25 + -1.25 + -2.5x + x2 = 0 + -1.25

Combine like terms: 1.25 + -1.25 = 0.00
0.00 + -2.5x + x2 = 0 + -1.25
-2.5x + x2 = 0 + -1.25

Combine like terms: 0 + -1.25 = -1.25
-2.5x + x2 = -1.25

The x term is -2.5x.  Take half its coefficient (-1.25).
Square it (1.5625) and add it to both sides.

Add '1.5625' to each side of the equation.
-2.5x + 1.5625 + x2 = -1.25 + 1.5625

Reorder the terms:
1.5625 + -2.5x + x2 = -1.25 + 1.5625

Combine like terms: -1.25 + 1.5625 = 0.3125
1.5625 + -2.5x + x2 = 0.3125

Factor a perfect square on the left side:
(x + -1.25)(x + -1.25) = 0.3125

Calculate the square root of the right side: 0.559016994

Break this problem into two subproblems by setting 
(x + -1.25) equal to 0.559016994 and -0.559016994.

Subproblem 1
x + -1.25 = 0.559016994

Simplifying
x + -1.25 = 0.559016994

Reorder the terms:
-1.25 + x = 0.559016994

Solving
-1.25 + x = 0.559016994

Solving for variable 'x'.

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

Add '1.25' to each side of the equation.
-1.25 + 1.25 + x = 0.559016994 + 1.25

Combine like terms: -1.25 + 1.25 = 0.00
0.00 + x = 0.559016994 + 1.25
x = 0.559016994 + 1.25

Combine like terms: 0.559016994 + 1.25 = 1.809016994
x = 1.809016994

Simplifying
x = 1.809016994

Subproblem 2
x + -1.25 = -0.559016994

Simplifying
x + -1.25 = -0.559016994

Reorder the terms:
-1.25 + x = -0.559016994

Solving
-1.25 + x = -0.559016994

Solving for variable 'x'.

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

Add '1.25' to each side of the equation.
-1.25 + 1.25 + x = -0.559016994 + 1.25

Combine like terms: -1.25 + 1.25 = 0.00
0.00 + x = -0.559016994 + 1.25
x = -0.559016994 + 1.25

Combine like terms: -0.559016994 + 1.25 = 0.690983006
x = 0.690983006

Simplifying
x = 0.690983006

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {1.809016994, 0.690983006}
Solution
x = {1.809016994, 0.690983006}