3x^3-17x^2=6x

Solution for 3x^3-17x^2=6x equation:

Simplifying
3x3 + -17x2 = 6x

Reorder the terms:
-17x2 + 3x3 = 6x

Solving
-17x2 + 3x3 = 6x

Solving for variable 'x'.

Reorder the terms:
-6x + -17x2 + 3x3 = 6x + -6x

Combine like terms: 6x + -6x = 0
-6x + -17x2 + 3x3 = 0

Factor out the Greatest Common Factor (GCF), 'x'.
x(-6 + -17x + 3x2) = 0

Factor a trinomial.
x((-1 + -3x)(6 + -1x)) = 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 '(-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 '(6 + -1x)' equal to zero and attempt to solve:

Simplifying
6 + -1x = 0

Solving
6 + -1x = 0

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

Add '-6' to each side of the equation.
6 + -6 + -1x = 0 + -6

Combine like terms: 6 + -6 = 0
0 + -1x = 0 + -6
-1x = 0 + -6

Combine like terms: 0 + -6 = -6
-1x = -6

Divide each side by '-1'.
x = 6

Simplifying
x = 6
Solution
x = {0, -0.3333333333, 6}