(3x-8)(x-1)=12

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Solution for (3x-8)(x-1)=12 equation: 


Simplifying
(3x + -8)(x + -1) = 12

Reorder the terms:
(-8 + 3x)(x + -1) = 12

Reorder the terms:
(-8 + 3x)(-1 + x) = 12

Multiply (-8 + 3x) * (-1 + x)
(-8(-1 + x) + 3x * (-1 + x)) = 12
((-1 * -8 + x * -8) + 3x * (-1 + x)) = 12
((8 + -8x) + 3x * (-1 + x)) = 12
(8 + -8x + (-1 * 3x + x * 3x)) = 12
(8 + -8x + (-3x + 3x2)) = 12

Combine like terms: -8x + -3x = -11x
(8 + -11x + 3x2) = 12

Solving
8 + -11x + 3x2 = 12

Solving for variable 'x'.

Reorder the terms:
8 + -12 + -11x + 3x2 = 12 + -12

Combine like terms: 8 + -12 = -4
-4 + -11x + 3x2 = 12 + -12

Combine like terms: 12 + -12 = 0
-4 + -11x + 3x2 = 0

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


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

Simplifying
-1 + -3x = 0

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

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

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

Divide each side by '-3'.
x = -0.3333333333

Simplifying
x = -0.3333333333

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 = {-0.3333333333, 4}

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