(3x+2)(x^2+2x)=

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Solution for (3x+2)(x^2+2x)= equation: 


Simplifying
(3x + 2)(x2 + 2x) = 0

Reorder the terms:
(2 + 3x)(x2 + 2x) = 0

Reorder the terms:
(2 + 3x)(2x + x2) = 0

Multiply (2 + 3x) * (2x + x2)
(2(2x + x2) + 3x * (2x + x2)) = 0
((2x * 2 + x2 * 2) + 3x * (2x + x2)) = 0
((4x + 2x2) + 3x * (2x + x2)) = 0
(4x + 2x2 + (2x * 3x + x2 * 3x)) = 0
(4x + 2x2 + (6x2 + 3x3)) = 0

Combine like terms: 2x2 + 6x2 = 8x2
(4x + 8x2 + 3x3) = 0

Solving
4x + 8x2 + 3x3 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), 'x'.
x(4 + 8x + 3x2) = 0

Factor a trinomial.
x((2 + 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 '(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 '(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, -2, -0.6666666667}

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