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

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


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

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

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

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

Combine like terms: 3x + 2x = 5x
x(2 + 5x + 3x2) = 0
(2 * x + 5x * x + 3x2 * x) = 0
(2x + 5x2 + 3x3) = 0

Solving
2x + 5x2 + 3x3 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), 'x'.
x(2 + 5x + 3x2) = 0

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

Simplifying
1 + x = 0

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

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

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

Simplifying
x = -1

Subproblem 3
Set the factor '(2 + 3x)' equal to zero and attempt to solve:

Simplifying
2 + 3x = 0

Solving
2 + 3x = 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 + 3x = 0 + -2

Combine like terms: 2 + -2 = 0
0 + 3x = 0 + -2
3x = 0 + -2

Combine like terms: 0 + -2 = -2
3x = -2

Divide each side by '3'.
x = -0.6666666667

Simplifying
x = -0.6666666667
Solution
x = {0, -1, -0.6666666667}

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