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

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Solution for (2x-1)(x-2)=(1-2x)(x+2) equation:


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

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

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

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

Combine like terms: -1x + -4x = -5x
(2 + -5x + 2x2) = (1 + -2x)(x + 2)

Reorder the terms:
2 + -5x + 2x2 = (1 + -2x)(2 + x)

Multiply (1 + -2x) * (2 + x)
2 + -5x + 2x2 = (1(2 + x) + -2x * (2 + x))
2 + -5x + 2x2 = ((2 * 1 + x * 1) + -2x * (2 + x))
2 + -5x + 2x2 = ((2 + 1x) + -2x * (2 + x))
2 + -5x + 2x2 = (2 + 1x + (2 * -2x + x * -2x))
2 + -5x + 2x2 = (2 + 1x + (-4x + -2x2))

Combine like terms: 1x + -4x = -3x
2 + -5x + 2x2 = (2 + -3x + -2x2)

Add '-2' to each side of the equation.
2 + -5x + -2 + 2x2 = 2 + -3x + -2 + -2x2

Reorder the terms:
2 + -2 + -5x + 2x2 = 2 + -3x + -2 + -2x2

Combine like terms: 2 + -2 = 0
0 + -5x + 2x2 = 2 + -3x + -2 + -2x2
-5x + 2x2 = 2 + -3x + -2 + -2x2

Reorder the terms:
-5x + 2x2 = 2 + -2 + -3x + -2x2

Combine like terms: 2 + -2 = 0
-5x + 2x2 = 0 + -3x + -2x2
-5x + 2x2 = -3x + -2x2

Solving
-5x + 2x2 = -3x + -2x2

Solving for variable 'x'.

Reorder the terms:
-5x + 3x + 2x2 + 2x2 = -3x + -2x2 + 3x + 2x2

Combine like terms: -5x + 3x = -2x
-2x + 2x2 + 2x2 = -3x + -2x2 + 3x + 2x2

Combine like terms: 2x2 + 2x2 = 4x2
-2x + 4x2 = -3x + -2x2 + 3x + 2x2

Reorder the terms:
-2x + 4x2 = -3x + 3x + -2x2 + 2x2

Combine like terms: -3x + 3x = 0
-2x + 4x2 = 0 + -2x2 + 2x2
-2x + 4x2 = -2x2 + 2x2

Combine like terms: -2x2 + 2x2 = 0
-2x + 4x2 = 0

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

Ignore the factor 2.

Subproblem 1
Set the factor 'x' equal to zero and attempt to solve:

Simplifying
x = 0

Solving
x = 0

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

Simplifying
x = 0

Subproblem 2
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
Solution
x = {0, 0.5}

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