8(x-2)*2x=20

Solution for 8(x-2)*2x=20 equation:

Simplifying
8(x + -2) * 2x = 20

Reorder the terms:
8(-2 + x) * 2x = 20

Reorder the terms for easier multiplication:
8 * 2x(-2 + x) = 20

Multiply 8 * 2
16x(-2 + x) = 20
(-2 * 16x + x * 16x) = 20
(-32x + 16x2) = 20

Solving
-32x + 16x2 = 20

Solving for variable 'x'.

Reorder the terms:
-20 + -32x + 16x2 = 20 + -20

Combine like terms: 20 + -20 = 0
-20 + -32x + 16x2 = 0

Factor out the Greatest Common Factor (GCF), '4'.
4(-5 + -8x + 4x2) = 0

Factor a trinomial.
4((-1 + -2x)(5 + -2x)) = 0

Ignore the factor 4.
Subproblem 1
Set the factor '(-1 + -2x)' equal to zero and attempt to solve:

Simplifying
-1 + -2x = 0

Solving
-1 + -2x = 0

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

Add '1' to each side of the equation.
-1 + 1 + -2x = 0 + 1

Combine like terms: -1 + 1 = 0
0 + -2x = 0 + 1
-2x = 0 + 1

Combine like terms: 0 + 1 = 1
-2x = 1

Divide each side by '-2'.
x = -0.5

Simplifying
x = -0.5
Subproblem 2
Set the factor '(5 + -2x)' equal to zero and attempt to solve:

Simplifying
5 + -2x = 0

Solving
5 + -2x = 0

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

Add '-5' to each side of the equation.
5 + -5 + -2x = 0 + -5

Combine like terms: 5 + -5 = 0
0 + -2x = 0 + -5
-2x = 0 + -5

Combine like terms: 0 + -5 = -5
-2x = -5

Divide each side by '-2'.
x = 2.5

Simplifying
x = 2.5
Solution
x = {-0.5, 2.5}