0=3x^3+22x^2-16x

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Solution for 0=3x^3+22x^2-16x equation: 


Simplifying
0 = 3x3 + 22x2 + -16x

Reorder the terms:
0 = -16x + 22x2 + 3x3

Solving
0 = -16x + 22x2 + 3x3

Solving for variable 'x'.
Remove the zero:
16x + -22x2 + -3x3 = -16x + 22x2 + 3x3 + 16x + -22x2 + -3x3

Reorder the terms:
16x + -22x2 + -3x3 = -16x + 16x + 22x2 + -22x2 + 3x3 + -3x3

Combine like terms: -16x + 16x = 0
16x + -22x2 + -3x3 = 0 + 22x2 + -22x2 + 3x3 + -3x3
16x + -22x2 + -3x3 = 22x2 + -22x2 + 3x3 + -3x3

Combine like terms: 22x2 + -22x2 = 0
16x + -22x2 + -3x3 = 0 + 3x3 + -3x3
16x + -22x2 + -3x3 = 3x3 + -3x3

Combine like terms: 3x3 + -3x3 = 0
16x + -22x2 + -3x3 = 0

Factor out the Greatest Common Factor (GCF), 'x'.
x(16 + -22x + -3x2) = 0

Factor a trinomial.
x((2 + -3x)(8 + x)) = 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 + -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

Subproblem 3
Set the factor '(8 + x)' equal to zero and attempt to solve:

Simplifying
8 + x = 0

Solving
8 + x = 0

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

Add '-8' to each side of the equation.
8 + -8 + x = 0 + -8

Combine like terms: 8 + -8 = 0
0 + x = 0 + -8
x = 0 + -8

Combine like terms: 0 + -8 = -8
x = -8

Simplifying
x = -8
Solution
x = {0, 0.6666666667, -8}

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