0=6x^3+22x^2-8x

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Solution for 0=6x^3+22x^2-8x equation: 


Simplifying
0 = 6x3 + 22x2 + -8x

Reorder the terms:
0 = -8x + 22x2 + 6x3

Solving
0 = -8x + 22x2 + 6x3

Solving for variable 'x'.
Remove the zero:
8x + -22x2 + -6x3 = -8x + 22x2 + 6x3 + 8x + -22x2 + -6x3

Reorder the terms:
8x + -22x2 + -6x3 = -8x + 8x + 22x2 + -22x2 + 6x3 + -6x3

Combine like terms: -8x + 8x = 0
8x + -22x2 + -6x3 = 0 + 22x2 + -22x2 + 6x3 + -6x3
8x + -22x2 + -6x3 = 22x2 + -22x2 + 6x3 + -6x3

Combine like terms: 22x2 + -22x2 = 0
8x + -22x2 + -6x3 = 0 + 6x3 + -6x3
8x + -22x2 + -6x3 = 6x3 + -6x3

Combine like terms: 6x3 + -6x3 = 0
8x + -22x2 + -6x3 = 0

Factor out the Greatest Common Factor (GCF), '2x'.
2x(4 + -11x + -3x2) = 0

Factor a trinomial.
2x((1 + -3x)(4 + x)) = 0

Ignore the factor 2.

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 '(4 + x)' equal to zero and attempt to solve:

Simplifying
4 + x = 0

Solving
4 + x = 0

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

Add '-4' to each side of the equation.
4 + -4 + x = 0 + -4

Combine like terms: 4 + -4 = 0
0 + x = 0 + -4
x = 0 + -4

Combine like terms: 0 + -4 = -4
x = -4

Simplifying
x = -4
Solution
x = {0, 0.3333333333, -4}

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