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

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Solution for x(3x+1)(2x-1)=0 equation: 


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

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

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

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

Combine like terms: 2x + -3x = -1x
x(-1 + -1x + 6x2) = 0
(-1 * x + -1x * x + 6x2 * x) = 0
(-1x + -1x2 + 6x3) = 0

Solving
-1x + -1x2 + 6x3 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), 'x'.
x(-1 + -1x + 6x2) = 0

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


Subproblem 1
Set the factor 'x' equal to zero and attempt to solve:

Simplifying
x = 0

Solving
x = 0

Move all terms containing x to the left, all other terms to the right.

Simplifying
x = 0

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

Subproblem 3
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, -0.3333333333, 0.5}

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