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

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


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

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

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

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

Solving for variable 'x'.

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

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

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

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

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

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


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

Simplifying
2 + -3x = 0

Solving
2 + -3x = 0

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

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

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

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

Divide each side by '-3'.
x = 0.6666666667

Simplifying
x = 0.6666666667

Subproblem 2
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
Solution
x = {0.6666666667, 1}

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