15u^2=8u-2u^3

Solution for 15u^2=8u-2u^3 equation:

Simplifying
15u2 = 8u + -2u3

Solving
15u2 = 8u + -2u3

Solving for variable 'u'.

Reorder the terms:
-8u + 15u2 + 2u3 = 8u + -2u3 + -8u + 2u3

Reorder the terms:
-8u + 15u2 + 2u3 = 8u + -8u + -2u3 + 2u3

Combine like terms: 8u + -8u = 0
-8u + 15u2 + 2u3 = 0 + -2u3 + 2u3
-8u + 15u2 + 2u3 = -2u3 + 2u3

Combine like terms: -2u3 + 2u3 = 0
-8u + 15u2 + 2u3 = 0

Factor out the Greatest Common Factor (GCF), 'u'.
u(-8 + 15u + 2u2) = 0

Factor a trinomial.
u((-8 + -1u)(1 + -2u)) = 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 '(-8 + -1u)' equal to zero and attempt to solve:

Simplifying
-8 + -1u = 0

Solving
-8 + -1u = 0

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

Add '8' to each side of the equation.
-8 + 8 + -1u = 0 + 8

Combine like terms: -8 + 8 = 0
0 + -1u = 0 + 8
-1u = 0 + 8

Combine like terms: 0 + 8 = 8
-1u = 8

Divide each side by '-1'.
u = -8

Simplifying
u = -8
Subproblem 3
Set the factor '(1 + -2u)' equal to zero and attempt to solve:

Simplifying
1 + -2u = 0

Solving
1 + -2u = 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 + -2u = 0 + -1

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

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

Divide each side by '-2'.
u = 0.5

Simplifying
u = 0.5
Solution
u = {0, -8, 0.5}