0=6x^3-x^2-40x

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Solution for 0=6x^3-x^2-40x equation: 


Simplifying
0 = 6x3 + -1x2 + -40x

Reorder the terms:
0 = -40x + -1x2 + 6x3

Solving
0 = -40x + -1x2 + 6x3

Solving for variable 'x'.
Remove the zero:
40x + x2 + -6x3 = -40x + -1x2 + 6x3 + 40x + x2 + -6x3

Reorder the terms:
40x + x2 + -6x3 = -40x + 40x + -1x2 + x2 + 6x3 + -6x3

Combine like terms: -40x + 40x = 0
40x + x2 + -6x3 = 0 + -1x2 + x2 + 6x3 + -6x3
40x + x2 + -6x3 = -1x2 + x2 + 6x3 + -6x3

Combine like terms: -1x2 + x2 = 0
40x + x2 + -6x3 = 0 + 6x3 + -6x3
40x + x2 + -6x3 = 6x3 + -6x3

Combine like terms: 6x3 + -6x3 = 0
40x + x2 + -6x3 = 0

Factor out the Greatest Common Factor (GCF), 'x'.
x(40 + x + -6x2) = 0

Factor a trinomial.
x((8 + -3x)(5 + 2x)) = 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 '(8 + -3x)' equal to zero and attempt to solve:

Simplifying
8 + -3x = 0

Solving
8 + -3x = 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 + -3x = 0 + -8

Combine like terms: 8 + -8 = 0
0 + -3x = 0 + -8
-3x = 0 + -8

Combine like terms: 0 + -8 = -8
-3x = -8

Divide each side by '-3'.
x = 2.666666667

Simplifying
x = 2.666666667

Subproblem 3
Set the factor '(5 + 2x)' equal to zero and attempt to solve:

Simplifying
5 + 2x = 0

Solving
5 + 2x = 0

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

Add '-5' to each side of the equation.
5 + -5 + 2x = 0 + -5

Combine like terms: 5 + -5 = 0
0 + 2x = 0 + -5
2x = 0 + -5

Combine like terms: 0 + -5 = -5
2x = -5

Divide each side by '2'.
x = -2.5

Simplifying
x = -2.5
Solution
x = {0, 2.666666667, -2.5}

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