5(2-x)3(4-2x)=20

Solution for 5(2-x)3(4-2x)=20 equation:

Simplifying
5(2 + -1x) * 3(4 + -2x) = 20

Reorder the terms for easier multiplication:
5 * 3(2 + -1x)(4 + -2x) = 20

Multiply 5 * 3
15(2 + -1x)(4 + -2x) = 20

Multiply (2 + -1x) * (4 + -2x)
15(2(4 + -2x) + -1x * (4 + -2x)) = 20
15((4 * 2 + -2x * 2) + -1x * (4 + -2x)) = 20
15((8 + -4x) + -1x * (4 + -2x)) = 20
15(8 + -4x + (4 * -1x + -2x * -1x)) = 20
15(8 + -4x + (-4x + 2x2)) = 20

Combine like terms: -4x + -4x = -8x
15(8 + -8x + 2x2) = 20
(8 * 15 + -8x * 15 + 2x2 * 15) = 20
(120 + -120x + 30x2) = 20

Solving
120 + -120x + 30x2 = 20

Solving for variable 'x'.

Reorder the terms:
120 + -20 + -120x + 30x2 = 20 + -20

Combine like terms: 120 + -20 = 100
100 + -120x + 30x2 = 20 + -20

Combine like terms: 20 + -20 = 0
100 + -120x + 30x2 = 0

Factor out the Greatest Common Factor (GCF), '10'.
10(10 + -12x + 3x2) = 0

Ignore the factor 10.
Subproblem 1
Set the factor '(10 + -12x + 3x2)' equal to zero and attempt to solve:

Simplifying
10 + -12x + 3x2 = 0

Solving
10 + -12x + 3x2 = 0

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

Divide each side by '3'.
3.333333333 + -4x + x2 = 0

Move the constant term to the right:

Add '-3.333333333' to each side of the equation.
3.333333333 + -4x + -3.333333333 + x2 = 0 + -3.333333333

Reorder the terms:
3.333333333 + -3.333333333 + -4x + x2 = 0 + -3.333333333

Combine like terms: 3.333333333 + -3.333333333 = 0.000000000
0.000000000 + -4x + x2 = 0 + -3.333333333
-4x + x2 = 0 + -3.333333333

Combine like terms: 0 + -3.333333333 = -3.333333333
-4x + x2 = -3.333333333

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 = -3.333333333 + 4

Reorder the terms:
4 + -4x + x2 = -3.333333333 + 4

Combine like terms: -3.333333333 + 4 = 0.666666667
4 + -4x + x2 = 0.666666667

Factor a perfect square on the left side:
(x + -2)(x + -2) = 0.666666667

Calculate the square root of the right side: 0.816496581

Break this problem into two subproblems by setting 
(x + -2) equal to 0.816496581 and -0.816496581.

Subproblem 1
x + -2 = 0.816496581

Simplifying
x + -2 = 0.816496581

Reorder the terms:
-2 + x = 0.816496581

Solving
-2 + x = 0.816496581

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 = 0.816496581 + 2

Combine like terms: -2 + 2 = 0
0 + x = 0.816496581 + 2
x = 0.816496581 + 2

Combine like terms: 0.816496581 + 2 = 2.816496581
x = 2.816496581

Simplifying
x = 2.816496581

Subproblem 2
x + -2 = -0.816496581

Simplifying
x + -2 = -0.816496581

Reorder the terms:
-2 + x = -0.816496581

Solving
-2 + x = -0.816496581

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 = -0.816496581 + 2

Combine like terms: -2 + 2 = 0
0 + x = -0.816496581 + 2
x = -0.816496581 + 2

Combine like terms: -0.816496581 + 2 = 1.183503419
x = 1.183503419

Simplifying
x = 1.183503419

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {2.816496581, 1.183503419}
Solution
x = {2.816496581, 1.183503419}