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

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


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

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

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

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

Combine like terms: 6x + 1x = 7x
x(2 + 7x + 3x2) = 0
(2 * x + 7x * x + 3x2 * x) = 0
(2x + 7x2 + 3x3) = 0

Solving
2x + 7x2 + 3x3 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), 'x'.
x(2 + 7x + 3x2) = 0

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

Simplifying
2 + x = 0

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

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

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

Simplifying
x = -2

Subproblem 3
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 = {0, -2, -0.3333333333}

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