10u^6-26u^5-12u^4=0

Solution for 10u^6-26u^5-12u^4=0 equation:

Simplifying
10u6 + -26u5 + -12u4 = 0

Reorder the terms:
-12u4 + -26u5 + 10u6 = 0

Solving
-12u4 + -26u5 + 10u6 = 0

Solving for variable 'u'.

Factor out the Greatest Common Factor (GCF), '2u4'.
2u4(-6 + -13u + 5u2) = 0

Factor a trinomial.
2u4((-2 + -5u)(3 + -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 '(-2 + -5u)' equal to zero and attempt to solve:

Simplifying
-2 + -5u = 0

Solving
-2 + -5u = 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 + -5u = 0 + 2

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

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

Divide each side by '-5'.
u = -0.4

Simplifying
u = -0.4
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 = {-0.4, 3}