3u^3=5u^2+2u

Solution for 3u^3=5u^2+2u equation:

Simplifying
3u3 = 5u2 + 2u

Reorder the terms:
3u3 = 2u + 5u2

Solving
3u3 = 2u + 5u2

Solving for variable 'u'.

Reorder the terms:
-2u + -5u2 + 3u3 = 2u + 5u2 + -2u + -5u2

Reorder the terms:
-2u + -5u2 + 3u3 = 2u + -2u + 5u2 + -5u2

Combine like terms: 2u + -2u = 0
-2u + -5u2 + 3u3 = 0 + 5u2 + -5u2
-2u + -5u2 + 3u3 = 5u2 + -5u2

Combine like terms: 5u2 + -5u2 = 0
-2u + -5u2 + 3u3 = 0

Factor out the Greatest Common Factor (GCF), 'u'.
u(-2 + -5u + 3u2) = 0

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

Simplifying
-1 + -3u = 0

Solving
-1 + -3u = 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 + -3u = 0 + 1

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

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

Divide each side by '-3'.
u = -0.3333333333

Simplifying
u = -0.3333333333
Subproblem 3
Set the factor '(2 + -1u)' equal to zero and attempt to solve:

Simplifying
2 + -1u = 0

Solving
2 + -1u = 0

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

Add '-2' to each side of the equation.
2 + -2 + -1u = 0 + -2

Combine like terms: 2 + -2 = 0
0 + -1u = 0 + -2
-1u = 0 + -2

Combine like terms: 0 + -2 = -2
-1u = -2

Divide each side by '-1'.
u = 2

Simplifying
u = 2
Solution
u = {0, -0.3333333333, 2}