6u^3=17u^2+3u

Solution for 6u^3=17u^2+3u equation:

Simplifying
6u3 = 17u2 + 3u

Reorder the terms:
6u3 = 3u + 17u2

Solving
6u3 = 3u + 17u2

Solving for variable 'u'.

Reorder the terms:
-3u + -17u2 + 6u3 = 3u + 17u2 + -3u + -17u2

Reorder the terms:
-3u + -17u2 + 6u3 = 3u + -3u + 17u2 + -17u2

Combine like terms: 3u + -3u = 0
-3u + -17u2 + 6u3 = 0 + 17u2 + -17u2
-3u + -17u2 + 6u3 = 17u2 + -17u2

Combine like terms: 17u2 + -17u2 = 0
-3u + -17u2 + 6u3 = 0

Factor out the Greatest Common Factor (GCF), 'u'.
u(-3 + -17u + 6u2) = 0

Factor a trinomial.
u((-1 + -6u)(3 + -1u)) = 0

Subproblem 1
Set the factor 'u' equal to zero and attempt to solve:

Simplifying
u = 0

Solving
u = 0

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

Simplifying
u = 0
Subproblem 2
Set the factor '(-1 + -6u)' equal to zero and attempt to solve:

Simplifying
-1 + -6u = 0

Solving
-1 + -6u = 0

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

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

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

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

Divide each side by '-6'.
u = -0.1666666667

Simplifying
u = -0.1666666667
Subproblem 3
Set the factor '(3 + -1u)' equal to zero and attempt to solve:

Simplifying
3 + -1u = 0

Solving
3 + -1u = 0

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

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

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

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

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

Simplifying
u = 3
Solution
u = {0, -0.1666666667, 3}