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

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

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

Reorder the terms:
-5x(-2 + 4x) = -2(3 + 6x)
(-2 * -5x + 4x * -5x) = -2(3 + 6x)
(10x + -20x2) = -2(3 + 6x)
10x + -20x2 = (3 * -2 + 6x * -2)
10x + -20x2 = (-6 + -12x)

Solving
10x + -20x2 = -6 + -12x

Solving for variable 'x'.

Reorder the terms:
6 + 10x + 12x + -20x2 = -6 + -12x + 6 + 12x

Combine like terms: 10x + 12x = 22x
6 + 22x + -20x2 = -6 + -12x + 6 + 12x

Reorder the terms:
6 + 22x + -20x2 = -6 + 6 + -12x + 12x

Combine like terms: -6 + 6 = 0
6 + 22x + -20x2 = 0 + -12x + 12x
6 + 22x + -20x2 = -12x + 12x

Combine like terms: -12x + 12x = 0
6 + 22x + -20x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(3 + 11x + -10x2) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(3 + 11x + -10x2)' equal to zero and attempt to solve:

Simplifying
3 + 11x + -10x2 = 0

Solving
3 + 11x + -10x2 = 0

Begin completing the square.  Divide all terms by
-10 the coefficient of the squared term: 

Divide each side by '-10'.
-0.3 + -1.1x + x2 = 0.0

Move the constant term to the right:

Add '0.3' to each side of the equation.
-0.3 + -1.1x + 0.3 + x2 = 0.0 + 0.3

Reorder the terms:
-0.3 + 0.3 + -1.1x + x2 = 0.0 + 0.3

Combine like terms: -0.3 + 0.3 = 0.0
0.0 + -1.1x + x2 = 0.0 + 0.3
-1.1x + x2 = 0.0 + 0.3

Combine like terms: 0.0 + 0.3 = 0.3
-1.1x + x2 = 0.3

The x term is -1.1x.  Take half its coefficient (-0.55).
Square it (0.3025) and add it to both sides.

Add '0.3025' to each side of the equation.
-1.1x + 0.3025 + x2 = 0.3 + 0.3025

Reorder the terms:
0.3025 + -1.1x + x2 = 0.3 + 0.3025

Combine like terms: 0.3 + 0.3025 = 0.6025
0.3025 + -1.1x + x2 = 0.6025

Factor a perfect square on the left side:
(x + -0.55)(x + -0.55) = 0.6025

Calculate the square root of the right side: 0.776208735

Break this problem into two subproblems by setting 
(x + -0.55) equal to 0.776208735 and -0.776208735.

Subproblem 1
x + -0.55 = 0.776208735

Simplifying
x + -0.55 = 0.776208735

Reorder the terms:
-0.55 + x = 0.776208735

Solving
-0.55 + x = 0.776208735

Solving for variable 'x'.

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

Add '0.55' to each side of the equation.
-0.55 + 0.55 + x = 0.776208735 + 0.55

Combine like terms: -0.55 + 0.55 = 0.00
0.00 + x = 0.776208735 + 0.55
x = 0.776208735 + 0.55

Combine like terms: 0.776208735 + 0.55 = 1.326208735
x = 1.326208735

Simplifying
x = 1.326208735

Subproblem 2
x + -0.55 = -0.776208735

Simplifying
x + -0.55 = -0.776208735

Reorder the terms:
-0.55 + x = -0.776208735

Solving
-0.55 + x = -0.776208735

Solving for variable 'x'.

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

Add '0.55' to each side of the equation.
-0.55 + 0.55 + x = -0.776208735 + 0.55

Combine like terms: -0.55 + 0.55 = 0.00
0.00 + x = -0.776208735 + 0.55
x = -0.776208735 + 0.55

Combine like terms: -0.776208735 + 0.55 = -0.226208735
x = -0.226208735

Simplifying
x = -0.226208735

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {1.326208735, -0.226208735}
Solution
x = {1.326208735, -0.226208735}