4u^6+6u^5-10u^4=

Solution for 4u^6+6u^5-10u^4= equation:

Simplifying
4u6 + 6u5 + -10u4 = 0

Reorder the terms:
-10u4 + 6u5 + 4u6 = 0

Solving
-10u4 + 6u5 + 4u6 = 0

Solving for variable 'u'.

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

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

Ignore the factor 2.
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 '(-5 + -2u)' equal to zero and attempt to solve:

Simplifying
-5 + -2u = 0

Solving
-5 + -2u = 0

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

Add '5' to each side of the equation.
-5 + 5 + -2u = 0 + 5

Combine like terms: -5 + 5 = 0
0 + -2u = 0 + 5
-2u = 0 + 5

Combine like terms: 0 + 5 = 5
-2u = 5

Divide each side by '-2'.
u = -2.5

Simplifying
u = -2.5
Subproblem 3
Set the factor '(1 + -1u)' equal to zero and attempt to solve:

Simplifying
1 + -1u = 0

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

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

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

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

Simplifying
u = 1
Solution
u = {-2.5, 1}