(x-1)(3x-4)=2

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Solution for (x-1)(3x-4)=2 equation: 


Simplifying
(x + -1)(3x + -4) = 2

Reorder the terms:
(-1 + x)(3x + -4) = 2

Reorder the terms:
(-1 + x)(-4 + 3x) = 2

Multiply (-1 + x) * (-4 + 3x)
(-1(-4 + 3x) + x(-4 + 3x)) = 2
((-4 * -1 + 3x * -1) + x(-4 + 3x)) = 2
((4 + -3x) + x(-4 + 3x)) = 2
(4 + -3x + (-4 * x + 3x * x)) = 2
(4 + -3x + (-4x + 3x2)) = 2

Combine like terms: -3x + -4x = -7x
(4 + -7x + 3x2) = 2

Solving
4 + -7x + 3x2 = 2

Solving for variable 'x'.

Reorder the terms:
4 + -2 + -7x + 3x2 = 2 + -2

Combine like terms: 4 + -2 = 2
2 + -7x + 3x2 = 2 + -2

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

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

Simplifying
2 + -1x = 0

Solving
2 + -1x = 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 + -1x = 0 + -2

Combine like terms: 2 + -2 = 0
0 + -1x = 0 + -2
-1x = 0 + -2

Combine like terms: 0 + -2 = -2
-1x = -2

Divide each side by '-1'.
x = 2

Simplifying
x = 2
Solution
x = {0.3333333333, 2}

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