(3x-2)(x-1)=2x+8

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Solution for (3x-2)(x-1)=2x+8 equation: 


Simplifying
(3x + -2)(x + -1) = 2x + 8

Reorder the terms:
(-2 + 3x)(x + -1) = 2x + 8

Reorder the terms:
(-2 + 3x)(-1 + x) = 2x + 8

Multiply (-2 + 3x) * (-1 + x)
(-2(-1 + x) + 3x * (-1 + x)) = 2x + 8
((-1 * -2 + x * -2) + 3x * (-1 + x)) = 2x + 8
((2 + -2x) + 3x * (-1 + x)) = 2x + 8
(2 + -2x + (-1 * 3x + x * 3x)) = 2x + 8
(2 + -2x + (-3x + 3x2)) = 2x + 8

Combine like terms: -2x + -3x = -5x
(2 + -5x + 3x2) = 2x + 8

Reorder the terms:
2 + -5x + 3x2 = 8 + 2x

Solving
2 + -5x + 3x2 = 8 + 2x

Solving for variable 'x'.

Reorder the terms:
2 + -8 + -5x + -2x + 3x2 = 8 + 2x + -8 + -2x

Combine like terms: 2 + -8 = -6
-6 + -5x + -2x + 3x2 = 8 + 2x + -8 + -2x

Combine like terms: -5x + -2x = -7x
-6 + -7x + 3x2 = 8 + 2x + -8 + -2x

Reorder the terms:
-6 + -7x + 3x2 = 8 + -8 + 2x + -2x

Combine like terms: 8 + -8 = 0
-6 + -7x + 3x2 = 0 + 2x + -2x
-6 + -7x + 3x2 = 2x + -2x

Combine like terms: 2x + -2x = 0
-6 + -7x + 3x2 = 0

Factor a trinomial.
(-2 + -3x)(3 + -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 '(3 + -1x)' equal to zero and attempt to solve:

Simplifying
3 + -1x = 0

Solving
3 + -1x = 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 + -1x = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -1x = 0 + -3
-1x = 0 + -3

Combine like terms: 0 + -3 = -3
-1x = -3

Divide each side by '-1'.
x = 3

Simplifying
x = 3
Solution
x = {-0.6666666667, 3}

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