2x(3x-4)-6x=10x+36

Solution for 2x(3x-4)-6x=10x+36 equation:

Simplifying
2x(3x + -4) + -6x = 10x + 36

Reorder the terms:
2x(-4 + 3x) + -6x = 10x + 36
(-4 * 2x + 3x * 2x) + -6x = 10x + 36
(-8x + 6x2) + -6x = 10x + 36

Reorder the terms:
-8x + -6x + 6x2 = 10x + 36

Combine like terms: -8x + -6x = -14x
-14x + 6x2 = 10x + 36

Reorder the terms:
-14x + 6x2 = 36 + 10x

Solving
-14x + 6x2 = 36 + 10x

Solving for variable 'x'.

Reorder the terms:
-36 + -14x + -10x + 6x2 = 36 + 10x + -36 + -10x

Combine like terms: -14x + -10x = -24x
-36 + -24x + 6x2 = 36 + 10x + -36 + -10x

Reorder the terms:
-36 + -24x + 6x2 = 36 + -36 + 10x + -10x

Combine like terms: 36 + -36 = 0
-36 + -24x + 6x2 = 0 + 10x + -10x
-36 + -24x + 6x2 = 10x + -10x

Combine like terms: 10x + -10x = 0
-36 + -24x + 6x2 = 0

Factor out the Greatest Common Factor (GCF), '6'.
6(-6 + -4x + x2) = 0

Ignore the factor 6.
Subproblem 1
Set the factor '(-6 + -4x + x2)' equal to zero and attempt to solve:

Simplifying
-6 + -4x + x2 = 0

Solving
-6 + -4x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '6' to each side of the equation.
-6 + -4x + 6 + x2 = 0 + 6

Reorder the terms:
-6 + 6 + -4x + x2 = 0 + 6

Combine like terms: -6 + 6 = 0
0 + -4x + x2 = 0 + 6
-4x + x2 = 0 + 6

Combine like terms: 0 + 6 = 6
-4x + x2 = 6

The x term is -4x.  Take half its coefficient (-2).
Square it (4) and add it to both sides.

Add '4' to each side of the equation.
-4x + 4 + x2 = 6 + 4

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

Combine like terms: 6 + 4 = 10
4 + -4x + x2 = 10

Factor a perfect square on the left side:
(x + -2)(x + -2) = 10

Calculate the square root of the right side: 3.16227766

Break this problem into two subproblems by setting 
(x + -2) equal to 3.16227766 and -3.16227766.

Subproblem 1
x + -2 = 3.16227766

Simplifying
x + -2 = 3.16227766

Reorder the terms:
-2 + x = 3.16227766

Solving
-2 + x = 3.16227766

Solving for variable 'x'.

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

Add '2' to each side of the equation.
-2 + 2 + x = 3.16227766 + 2

Combine like terms: -2 + 2 = 0
0 + x = 3.16227766 + 2
x = 3.16227766 + 2

Combine like terms: 3.16227766 + 2 = 5.16227766
x = 5.16227766

Simplifying
x = 5.16227766

Subproblem 2
x + -2 = -3.16227766

Simplifying
x + -2 = -3.16227766

Reorder the terms:
-2 + x = -3.16227766

Solving
-2 + x = -3.16227766

Solving for variable 'x'.

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

Add '2' to each side of the equation.
-2 + 2 + x = -3.16227766 + 2

Combine like terms: -2 + 2 = 0
0 + x = -3.16227766 + 2
x = -3.16227766 + 2

Combine like terms: -3.16227766 + 2 = -1.16227766
x = -1.16227766

Simplifying
x = -1.16227766

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {5.16227766, -1.16227766}
Solution
x = {5.16227766, -1.16227766}