2=(4x-2)(2-x)

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

Simplifying
2 = (4x + -2)(2 + -1x)

Reorder the terms:
2 = (-2 + 4x)(2 + -1x)

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

Combine like terms: 2x + 8x = 10x
2 = (-4 + 10x + -4x2)

Solving
2 = -4 + 10x + -4x2

Solving for variable 'x'.

Combine like terms: 2 + 4 = 6
6 + -10x + 4x2 = -4 + 10x + -4x2 + 4 + -10x + 4x2

Reorder the terms:
6 + -10x + 4x2 = -4 + 4 + 10x + -10x + -4x2 + 4x2

Combine like terms: -4 + 4 = 0
6 + -10x + 4x2 = 0 + 10x + -10x + -4x2 + 4x2
6 + -10x + 4x2 = 10x + -10x + -4x2 + 4x2

Combine like terms: 10x + -10x = 0
6 + -10x + 4x2 = 0 + -4x2 + 4x2
6 + -10x + 4x2 = -4x2 + 4x2

Combine like terms: -4x2 + 4x2 = 0
6 + -10x + 4x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(3 + -5x + 2x2) = 0

Factor a trinomial.
2((1 + -1x)(3 + -2x)) = 0

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

Simplifying
1 + -1x = 0

Solving
1 + -1x = 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 + -1x = 0 + -1

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

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

Divide each side by '-1'.
x = 1

Simplifying
x = 1
Subproblem 2
Set the factor '(3 + -2x)' equal to zero and attempt to solve:

Simplifying
3 + -2x = 0

Solving
3 + -2x = 0

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

Add '-3' to each side of the equation.
3 + -3 + -2x = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -2x = 0 + -3
-2x = 0 + -3

Combine like terms: 0 + -3 = -3
-2x = -3

Divide each side by '-2'.
x = 1.5

Simplifying
x = 1.5
Solution
x = {1, 1.5}