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

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


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

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

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

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

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

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

Solving
-1 + 1x + 6x2 = 3 + 6x

Solving for variable 'x'.

Reorder the terms:
-1 + -3 + 1x + -6x + 6x2 = 3 + 6x + -3 + -6x

Combine like terms: -1 + -3 = -4
-4 + 1x + -6x + 6x2 = 3 + 6x + -3 + -6x

Combine like terms: 1x + -6x = -5x
-4 + -5x + 6x2 = 3 + 6x + -3 + -6x

Reorder the terms:
-4 + -5x + 6x2 = 3 + -3 + 6x + -6x

Combine like terms: 3 + -3 = 0
-4 + -5x + 6x2 = 0 + 6x + -6x
-4 + -5x + 6x2 = 6x + -6x

Combine like terms: 6x + -6x = 0
-4 + -5x + 6x2 = 0

Factor a trinomial.
(-1 + -2x)(4 + -3x) = 0


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

Simplifying
-1 + -2x = 0

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

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

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

Divide each side by '-2'.
x = -0.5

Simplifying
x = -0.5

Subproblem 2
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
Solution
x = {-0.5, 1.333333333}

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