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

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


Simplifying
0 = (3x + -1)(2x + 1)

Reorder the terms:
0 = (-1 + 3x)(2x + 1)

Reorder the terms:
0 = (-1 + 3x)(1 + 2x)

Multiply (-1 + 3x) * (1 + 2x)
0 = (-1(1 + 2x) + 3x * (1 + 2x))
0 = ((1 * -1 + 2x * -1) + 3x * (1 + 2x))
0 = ((-1 + -2x) + 3x * (1 + 2x))
0 = (-1 + -2x + (1 * 3x + 2x * 3x))
0 = (-1 + -2x + (3x + 6x2))

Combine like terms: -2x + 3x = 1x
0 = (-1 + 1x + 6x2)

Solving
0 = -1 + 1x + 6x2

Solving for variable 'x'.

Combine like terms: 0 + 1 = 1
1 + -1x + -6x2 = -1 + 1x + 6x2 + 1 + -1x + -6x2

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

Combine like terms: -1 + 1 = 0
1 + -1x + -6x2 = 0 + 1x + -1x + 6x2 + -6x2
1 + -1x + -6x2 = 1x + -1x + 6x2 + -6x2

Combine like terms: 1x + -1x = 0
1 + -1x + -6x2 = 0 + 6x2 + -6x2
1 + -1x + -6x2 = 6x2 + -6x2

Combine like terms: 6x2 + -6x2 = 0
1 + -1x + -6x2 = 0

Factor a trinomial.
(1 + -3x)(1 + 2x) = 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 '(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
Solution
x = {0.3333333333, -0.5}

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