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

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


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

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

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

Multiply (-1 + 3x) * (4 + x)
(-1(4 + x) + 3x * (4 + x)) = 2(3x + -1)
((4 * -1 + x * -1) + 3x * (4 + x)) = 2(3x + -1)
((-4 + -1x) + 3x * (4 + x)) = 2(3x + -1)
(-4 + -1x + (4 * 3x + x * 3x)) = 2(3x + -1)
(-4 + -1x + (12x + 3x2)) = 2(3x + -1)

Combine like terms: -1x + 12x = 11x
(-4 + 11x + 3x2) = 2(3x + -1)

Reorder the terms:
-4 + 11x + 3x2 = 2(-1 + 3x)
-4 + 11x + 3x2 = (-1 * 2 + 3x * 2)
-4 + 11x + 3x2 = (-2 + 6x)

Solving
-4 + 11x + 3x2 = -2 + 6x

Solving for variable 'x'.

Reorder the terms:
-4 + 2 + 11x + -6x + 3x2 = -2 + 6x + 2 + -6x

Combine like terms: -4 + 2 = -2
-2 + 11x + -6x + 3x2 = -2 + 6x + 2 + -6x

Combine like terms: 11x + -6x = 5x
-2 + 5x + 3x2 = -2 + 6x + 2 + -6x

Reorder the terms:
-2 + 5x + 3x2 = -2 + 2 + 6x + -6x

Combine like terms: -2 + 2 = 0
-2 + 5x + 3x2 = 0 + 6x + -6x
-2 + 5x + 3x2 = 6x + -6x

Combine like terms: 6x + -6x = 0
-2 + 5x + 3x2 = 0

Factor a trinomial.
(-2 + -1x)(1 + -3x) = 0


Subproblem 1
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

Subproblem 2
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
Solution
x = {-2, 0.3333333333}

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