0=6x^3+34x^2+40x

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Solution for 0=6x^3+34x^2+40x equation: 


Simplifying
0 = 6x3 + 34x2 + 40x

Reorder the terms:
0 = 40x + 34x2 + 6x3

Solving
0 = 40x + 34x2 + 6x3

Solving for variable 'x'.
Remove the zero:
-40x + -34x2 + -6x3 = 40x + 34x2 + 6x3 + -40x + -34x2 + -6x3

Reorder the terms:
-40x + -34x2 + -6x3 = 40x + -40x + 34x2 + -34x2 + 6x3 + -6x3

Combine like terms: 40x + -40x = 0
-40x + -34x2 + -6x3 = 0 + 34x2 + -34x2 + 6x3 + -6x3
-40x + -34x2 + -6x3 = 34x2 + -34x2 + 6x3 + -6x3

Combine like terms: 34x2 + -34x2 = 0
-40x + -34x2 + -6x3 = 0 + 6x3 + -6x3
-40x + -34x2 + -6x3 = 6x3 + -6x3

Combine like terms: 6x3 + -6x3 = 0
-40x + -34x2 + -6x3 = 0

Factor out the Greatest Common Factor (GCF), '-2x'.
-2x(20 + 17x + 3x2) = 0

Factor a trinomial.
-2x((4 + x)(5 + 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 '(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

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

Simplifying
5 + 3x = 0

Solving
5 + 3x = 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 + 3x = 0 + -5

Combine like terms: 5 + -5 = 0
0 + 3x = 0 + -5
3x = 0 + -5

Combine like terms: 0 + -5 = -5
3x = -5

Divide each side by '3'.
x = -1.666666667

Simplifying
x = -1.666666667
Solution
x = {0, -4, -1.666666667}

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