6x^3-22x^2-100x=20x

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Solution for 6x^3-22x^2-100x=20x equation: 


Simplifying
6x3 + -22x2 + -100x = 20x

Reorder the terms:
-100x + -22x2 + 6x3 = 20x

Solving
-100x + -22x2 + 6x3 = 20x

Solving for variable 'x'.

Reorder the terms:
-100x + -20x + -22x2 + 6x3 = 20x + -20x

Combine like terms: -100x + -20x = -120x
-120x + -22x2 + 6x3 = 20x + -20x

Combine like terms: 20x + -20x = 0
-120x + -22x2 + 6x3 = 0

Factor out the Greatest Common Factor (GCF), '2x'.
2x(-60 + -11x + 3x2) = 0

Factor a trinomial.
2x((-3 + -1x)(20 + -3x)) = 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 '(-3 + -1x)' equal to zero and attempt to solve:

Simplifying
-3 + -1x = 0

Solving
-3 + -1x = 0

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

Add '3' to each side of the equation.
-3 + 3 + -1x = 0 + 3

Combine like terms: -3 + 3 = 0
0 + -1x = 0 + 3
-1x = 0 + 3

Combine like terms: 0 + 3 = 3
-1x = 3

Divide each side by '-1'.
x = -3

Simplifying
x = -3

Subproblem 3
Set the factor '(20 + -3x)' equal to zero and attempt to solve:

Simplifying
20 + -3x = 0

Solving
20 + -3x = 0

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

Add '-20' to each side of the equation.
20 + -20 + -3x = 0 + -20

Combine like terms: 20 + -20 = 0
0 + -3x = 0 + -20
-3x = 0 + -20

Combine like terms: 0 + -20 = -20
-3x = -20

Divide each side by '-3'.
x = 6.666666667

Simplifying
x = 6.666666667
Solution
x = {0, -3, 6.666666667}

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