0=(3x-2)(x-2)

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Solution for 0=(3x-2)(x-2) equation: 


Simplifying
0 = (3x + -2)(x + -2)

Reorder the terms:
0 = (-2 + 3x)(x + -2)

Reorder the terms:
0 = (-2 + 3x)(-2 + x)

Multiply (-2 + 3x) * (-2 + x)
0 = (-2(-2 + x) + 3x * (-2 + x))
0 = ((-2 * -2 + x * -2) + 3x * (-2 + x))
0 = ((4 + -2x) + 3x * (-2 + x))
0 = (4 + -2x + (-2 * 3x + x * 3x))
0 = (4 + -2x + (-6x + 3x2))

Combine like terms: -2x + -6x = -8x
0 = (4 + -8x + 3x2)

Solving
0 = 4 + -8x + 3x2

Solving for variable 'x'.

Combine like terms: 0 + -4 = -4
-4 + 8x + -3x2 = 4 + -8x + 3x2 + -4 + 8x + -3x2

Reorder the terms:
-4 + 8x + -3x2 = 4 + -4 + -8x + 8x + 3x2 + -3x2

Combine like terms: 4 + -4 = 0
-4 + 8x + -3x2 = 0 + -8x + 8x + 3x2 + -3x2
-4 + 8x + -3x2 = -8x + 8x + 3x2 + -3x2

Combine like terms: -8x + 8x = 0
-4 + 8x + -3x2 = 0 + 3x2 + -3x2
-4 + 8x + -3x2 = 3x2 + -3x2

Combine like terms: 3x2 + -3x2 = 0
-4 + 8x + -3x2 = 0

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


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

Simplifying
-2 + x = 0

Solving
-2 + x = 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 + x = 0 + 2

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

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

Simplifying
x = 2

Subproblem 2
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
Solution
x = {2, 0.6666666667}

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