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

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

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

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

Solving
10x + -2x2 = 6 + -12x

Solving for variable 'x'.

Reorder the terms:
-6 + 10x + 12x + -2x2 = 6 + -12x + -6 + 12x

Combine like terms: 10x + 12x = 22x
-6 + 22x + -2x2 = 6 + -12x + -6 + 12x

Reorder the terms:
-6 + 22x + -2x2 = 6 + -6 + -12x + 12x

Combine like terms: 6 + -6 = 0
-6 + 22x + -2x2 = 0 + -12x + 12x
-6 + 22x + -2x2 = -12x + 12x

Combine like terms: -12x + 12x = 0
-6 + 22x + -2x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-3 + 11x + -1x2) = 0

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

Simplifying
-3 + 11x + -1x2 = 0

Solving
-3 + 11x + -1x2 = 0

Begin completing the square.  Divide all terms by
-1 the coefficient of the squared term: 

Divide each side by '-1'.
3 + -11x + x2 = 0

Move the constant term to the right:

Add '-3' to each side of the equation.
3 + -11x + -3 + x2 = 0 + -3

Reorder the terms:
3 + -3 + -11x + x2 = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -11x + x2 = 0 + -3
-11x + x2 = 0 + -3

Combine like terms: 0 + -3 = -3
-11x + x2 = -3

The x term is -11x.  Take half its coefficient (-5.5).
Square it (30.25) and add it to both sides.

Add '30.25' to each side of the equation.
-11x + 30.25 + x2 = -3 + 30.25

Reorder the terms:
30.25 + -11x + x2 = -3 + 30.25

Combine like terms: -3 + 30.25 = 27.25
30.25 + -11x + x2 = 27.25

Factor a perfect square on the left side:
(x + -5.5)(x + -5.5) = 27.25

Calculate the square root of the right side: 5.220153254

Break this problem into two subproblems by setting 
(x + -5.5) equal to 5.220153254 and -5.220153254.

Subproblem 1
x + -5.5 = 5.220153254

Simplifying
x + -5.5 = 5.220153254

Reorder the terms:
-5.5 + x = 5.220153254

Solving
-5.5 + x = 5.220153254

Solving for variable 'x'.

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

Add '5.5' to each side of the equation.
-5.5 + 5.5 + x = 5.220153254 + 5.5

Combine like terms: -5.5 + 5.5 = 0.0
0.0 + x = 5.220153254 + 5.5
x = 5.220153254 + 5.5

Combine like terms: 5.220153254 + 5.5 = 10.720153254
x = 10.720153254

Simplifying
x = 10.720153254

Subproblem 2
x + -5.5 = -5.220153254

Simplifying
x + -5.5 = -5.220153254

Reorder the terms:
-5.5 + x = -5.220153254

Solving
-5.5 + x = -5.220153254

Solving for variable 'x'.

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

Add '5.5' to each side of the equation.
-5.5 + 5.5 + x = -5.220153254 + 5.5

Combine like terms: -5.5 + 5.5 = 0.0
0.0 + x = -5.220153254 + 5.5
x = -5.220153254 + 5.5

Combine like terms: -5.220153254 + 5.5 = 0.279846746
x = 0.279846746

Simplifying
x = 0.279846746

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {10.720153254, 0.279846746}
Solution
x = {10.720153254, 0.279846746}