(3x-1)(x-2)=22

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Solution for (3x-1)(x-2)=22 equation: 


Simplifying
(3x + -1)(x + -2) = 22

Reorder the terms:
(-1 + 3x)(x + -2) = 22

Reorder the terms:
(-1 + 3x)(-2 + x) = 22

Multiply (-1 + 3x) * (-2 + x)
(-1(-2 + x) + 3x * (-2 + x)) = 22
((-2 * -1 + x * -1) + 3x * (-2 + x)) = 22
((2 + -1x) + 3x * (-2 + x)) = 22
(2 + -1x + (-2 * 3x + x * 3x)) = 22
(2 + -1x + (-6x + 3x2)) = 22

Combine like terms: -1x + -6x = -7x
(2 + -7x + 3x2) = 22

Solving
2 + -7x + 3x2 = 22

Solving for variable 'x'.

Reorder the terms:
2 + -22 + -7x + 3x2 = 22 + -22

Combine like terms: 2 + -22 = -20
-20 + -7x + 3x2 = 22 + -22

Combine like terms: 22 + -22 = 0
-20 + -7x + 3x2 = 0

Factor a trinomial.
(-5 + -3x)(4 + -1x) = 0


Subproblem 1
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

Subproblem 2
Set the factor '(4 + -1x)' equal to zero and attempt to solve:

Simplifying
4 + -1x = 0

Solving
4 + -1x = 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 + -1x = 0 + -4

Combine like terms: 4 + -4 = 0
0 + -1x = 0 + -4
-1x = 0 + -4

Combine like terms: 0 + -4 = -4
-1x = -4

Divide each side by '-1'.
x = 4

Simplifying
x = 4
Solution
x = {-1.666666667, 4}

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