2x(5x-4)-6(6-3x)=

Solution for 2x(5x-4)-6(6-3x)= equation:

Simplifying
2x(5x + -4) + -6(6 + -3x) = 0

Reorder the terms:
2x(-4 + 5x) + -6(6 + -3x) = 0
(-4 * 2x + 5x * 2x) + -6(6 + -3x) = 0
(-8x + 10x2) + -6(6 + -3x) = 0
-8x + 10x2 + (6 * -6 + -3x * -6) = 0
-8x + 10x2 + (-36 + 18x) = 0

Reorder the terms:
-36 + -8x + 18x + 10x2 = 0

Combine like terms: -8x + 18x = 10x
-36 + 10x + 10x2 = 0

Solving
-36 + 10x + 10x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '2'.
2(-18 + 5x + 5x2) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(-18 + 5x + 5x2)' equal to zero and attempt to solve:

Simplifying
-18 + 5x + 5x2 = 0

Solving
-18 + 5x + 5x2 = 0

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

Divide each side by '5'.
-3.6 + x + x2 = 0

Move the constant term to the right:

Add '3.6' to each side of the equation.
-3.6 + x + 3.6 + x2 = 0 + 3.6

Reorder the terms:
-3.6 + 3.6 + x + x2 = 0 + 3.6

Combine like terms: -3.6 + 3.6 = 0.0
0.0 + x + x2 = 0 + 3.6
x + x2 = 0 + 3.6

Combine like terms: 0 + 3.6 = 3.6
x + x2 = 3.6

The x term is x.  Take half its coefficient (0.5).
Square it (0.25) and add it to both sides.

Add '0.25' to each side of the equation.
 + 0.25 + x2 = 3.6 + 0.25

Combine like terms:  + 0.25 = 1.25
1.25 + x2 = 3.6 + 0.25

Combine like terms: 3.6 + 0.25 = 3.85
1.25 + x2 = 3.85

Factor a perfect square on the left side:
(x + 0.5)(x + 0.5) = 3.85

Calculate the square root of the right side: 1.962141687

Break this problem into two subproblems by setting 
(x + 0.5) equal to 1.962141687 and -1.962141687.

Subproblem 1
x + 0.5 = 1.962141687

Simplifying
x + 0.5 = 1.962141687

Reorder the terms:
0.5 + x = 1.962141687

Solving
0.5 + x = 1.962141687

Solving for variable 'x'.

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

Add '-0.5' to each side of the equation.
0.5 + -0.5 + x = 1.962141687 + -0.5

Combine like terms: 0.5 + -0.5 = 0.0
0.0 + x = 1.962141687 + -0.5
x = 1.962141687 + -0.5

Combine like terms: 1.962141687 + -0.5 = 1.462141687
x = 1.462141687

Simplifying
x = 1.462141687

Subproblem 2
x + 0.5 = -1.962141687

Simplifying
x + 0.5 = -1.962141687

Reorder the terms:
0.5 + x = -1.962141687

Solving
0.5 + x = -1.962141687

Solving for variable 'x'.

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

Add '-0.5' to each side of the equation.
0.5 + -0.5 + x = -1.962141687 + -0.5

Combine like terms: 0.5 + -0.5 = 0.0
0.0 + x = -1.962141687 + -0.5
x = -1.962141687 + -0.5

Combine like terms: -1.962141687 + -0.5 = -2.462141687
x = -2.462141687

Simplifying
x = -2.462141687

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {1.462141687, -2.462141687}
Solution
x = {1.462141687, -2.462141687}