10u^6-15u^5-45u^4=0

Solution for 10u^6-15u^5-45u^4=0 equation:

Simplifying
10u6 + -15u5 + -45u4 = 0

Reorder the terms:
-45u4 + -15u5 + 10u6 = 0

Solving
-45u4 + -15u5 + 10u6 = 0

Solving for variable 'u'.

Factor out the Greatest Common Factor (GCF), '5u4'.
5u4(-9 + -3u + 2u2) = 0

Factor a trinomial.
5u4((-3 + -2u)(3 + -1u)) = 0

Ignore the factor 5.
Subproblem 1
Set the factor 'u4' equal to zero and attempt to solve:

Simplifying
u4 = 0

Solving
u4 = 0

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

Simplifying
u4 = 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 + -2u)' equal to zero and attempt to solve:

Simplifying
-3 + -2u = 0

Solving
-3 + -2u = 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 + -2u = 0 + 3

Combine like terms: -3 + 3 = 0
0 + -2u = 0 + 3
-2u = 0 + 3

Combine like terms: 0 + 3 = 3
-2u = 3

Divide each side by '-2'.
u = -1.5

Simplifying
u = -1.5
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 = {-1.5, 3}