(3x-1)(2-x)=2(x-1)

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Solution for (3x-1)(2-x)=2(x-1) equation:


Simplifying
(3x + -1)(2 + -1x) = 2(x + -1)

Reorder the terms:
(-1 + 3x)(2 + -1x) = 2(x + -1)

Multiply (-1 + 3x) * (2 + -1x)
(-1(2 + -1x) + 3x * (2 + -1x)) = 2(x + -1)
((2 * -1 + -1x * -1) + 3x * (2 + -1x)) = 2(x + -1)
((-2 + 1x) + 3x * (2 + -1x)) = 2(x + -1)
(-2 + 1x + (2 * 3x + -1x * 3x)) = 2(x + -1)
(-2 + 1x + (6x + -3x2)) = 2(x + -1)

Combine like terms: 1x + 6x = 7x
(-2 + 7x + -3x2) = 2(x + -1)

Reorder the terms:
-2 + 7x + -3x2 = 2(-1 + x)
-2 + 7x + -3x2 = (-1 * 2 + x * 2)
-2 + 7x + -3x2 = (-2 + 2x)

Add '2' to each side of the equation.
-2 + 7x + 2 + -3x2 = -2 + 2 + 2x

Reorder the terms:
-2 + 2 + 7x + -3x2 = -2 + 2 + 2x

Combine like terms: -2 + 2 = 0
0 + 7x + -3x2 = -2 + 2 + 2x
7x + -3x2 = -2 + 2 + 2x

Combine like terms: -2 + 2 = 0
7x + -3x2 = 0 + 2x
7x + -3x2 = 2x

Solving
7x + -3x2 = 2x

Solving for variable 'x'.

Reorder the terms:
7x + -2x + -3x2 = 2x + -2x

Combine like terms: 7x + -2x = 5x
5x + -3x2 = 2x + -2x

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

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


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 '(5 + -3x)' equal to zero and attempt to solve:

Simplifying
5 + -3x = 0

Solving
5 + -3x = 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 + -3x = 0 + -5

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

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

Divide each side by '-3'.
x = 1.666666667

Simplifying
x = 1.666666667
Solution
x = {0, 1.666666667}

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