u^3+14u^2=32u

Solution for u^3+14u^2=32u equation:

Simplifying
u3 + 14u2 = 32u

Reorder the terms:
14u2 + u3 = 32u

Solving
14u2 + u3 = 32u

Solving for variable 'u'.

Reorder the terms:
-32u + 14u2 + u3 = 32u + -32u

Combine like terms: 32u + -32u = 0
-32u + 14u2 + u3 = 0

Factor out the Greatest Common Factor (GCF), 'u'.
u(-32 + 14u + u2) = 0

Factor a trinomial.
u((-16 + -1u)(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 '(-16 + -1u)' equal to zero and attempt to solve:

Simplifying
-16 + -1u = 0

Solving
-16 + -1u = 0

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

Add '16' to each side of the equation.
-16 + 16 + -1u = 0 + 16

Combine like terms: -16 + 16 = 0
0 + -1u = 0 + 16
-1u = 0 + 16

Combine like terms: 0 + 16 = 16
-1u = 16

Divide each side by '-1'.
u = -16

Simplifying
u = -16
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, -16, 2}