(3x-2)(x-1)=14

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Solution for (3x-2)(x-1)=14 equation: 


Simplifying
(3x + -2)(x + -1) = 14

Reorder the terms:
(-2 + 3x)(x + -1) = 14

Reorder the terms:
(-2 + 3x)(-1 + x) = 14

Multiply (-2 + 3x) * (-1 + x)
(-2(-1 + x) + 3x * (-1 + x)) = 14
((-1 * -2 + x * -2) + 3x * (-1 + x)) = 14
((2 + -2x) + 3x * (-1 + x)) = 14
(2 + -2x + (-1 * 3x + x * 3x)) = 14
(2 + -2x + (-3x + 3x2)) = 14

Combine like terms: -2x + -3x = -5x
(2 + -5x + 3x2) = 14

Solving
2 + -5x + 3x2 = 14

Solving for variable 'x'.

Reorder the terms:
2 + -14 + -5x + 3x2 = 14 + -14

Combine like terms: 2 + -14 = -12
-12 + -5x + 3x2 = 14 + -14

Combine like terms: 14 + -14 = 0
-12 + -5x + 3x2 = 0

Factor a trinomial.
(-4 + -3x)(3 + -1x) = 0


Subproblem 1
Set the factor '(-4 + -3x)' equal to zero and attempt to solve:

Simplifying
-4 + -3x = 0

Solving
-4 + -3x = 0

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

Add '4' to each side of the equation.
-4 + 4 + -3x = 0 + 4

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

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

Divide each side by '-3'.
x = -1.333333333

Simplifying
x = -1.333333333

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 = {-1.333333333, 3}

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