7u^5-42u^4+63u^3=0

Solution for 7u^5-42u^4+63u^3=0 equation:

Simplifying
7u5 + -42u4 + 63u3 = 0

Reorder the terms:
63u3 + -42u4 + 7u5 = 0

Solving
63u3 + -42u4 + 7u5 = 0

Solving for variable 'u'.

Factor out the Greatest Common Factor (GCF), '7u3'.
7u3(9 + -6u + u2) = 0

Factor a trinomial.
7u3((3 + -1u)(3 + -1u)) = 0

Ignore the factor 7.
Subproblem 1
Set the factor 'u3' equal to zero and attempt to solve:

Simplifying
u3 = 0

Solving
u3 = 0

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

Simplifying
u3 = 0

The solution to this equation could not be determined.

This subproblem is being ignored because a solution could not be determined.
Subproblem 2
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
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 = {3, 3}