4u^7+26u^6-12u^5=

Solution for 4u^7+26u^6-12u^5= equation:

Simplifying
4u7 + 26u6 + -12u5 = 0

Reorder the terms:
-12u5 + 26u6 + 4u7 = 0

Solving
-12u5 + 26u6 + 4u7 = 0

Solving for variable 'u'.

Factor out the Greatest Common Factor (GCF), '2u5'.
2u5(-6 + 13u + 2u2) = 0

Ignore the factor 2.
Subproblem 1
Set the factor 'u5' equal to zero and attempt to solve:

Simplifying
u5 = 0

Solving
u5 = 0

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

Simplifying
u5 = 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 '(-6 + 13u + 2u2)' equal to zero and attempt to solve:

Simplifying
-6 + 13u + 2u2 = 0

Solving
-6 + 13u + 2u2 = 0

Begin completing the square.  Divide all terms by
2 the coefficient of the squared term: 

Divide each side by '2'.
-3 + 6.5u + u2 = 0

Move the constant term to the right:

Add '3' to each side of the equation.
-3 + 6.5u + 3 + u2 = 0 + 3

Reorder the terms:
-3 + 3 + 6.5u + u2 = 0 + 3

Combine like terms: -3 + 3 = 0
0 + 6.5u + u2 = 0 + 3
6.5u + u2 = 0 + 3

Combine like terms: 0 + 3 = 3
6.5u + u2 = 3

The u term is 6.5u.  Take half its coefficient (3.25).
Square it (10.5625) and add it to both sides.

Add '10.5625' to each side of the equation.
6.5u + 10.5625 + u2 = 3 + 10.5625

Reorder the terms:
10.5625 + 6.5u + u2 = 3 + 10.5625

Combine like terms: 3 + 10.5625 = 13.5625
10.5625 + 6.5u + u2 = 13.5625

Factor a perfect square on the left side:
(u + 3.25)(u + 3.25) = 13.5625

Calculate the square root of the right side: 3.682729966

Break this problem into two subproblems by setting 
(u + 3.25) equal to 3.682729966 and -3.682729966.

Subproblem 1
u + 3.25 = 3.682729966

Simplifying
u + 3.25 = 3.682729966

Reorder the terms:
3.25 + u = 3.682729966

Solving
3.25 + u = 3.682729966

Solving for variable 'u'.

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

Add '-3.25' to each side of the equation.
3.25 + -3.25 + u = 3.682729966 + -3.25

Combine like terms: 3.25 + -3.25 = 0.00
0.00 + u = 3.682729966 + -3.25
u = 3.682729966 + -3.25

Combine like terms: 3.682729966 + -3.25 = 0.432729966
u = 0.432729966

Simplifying
u = 0.432729966

Subproblem 2
u + 3.25 = -3.682729966

Simplifying
u + 3.25 = -3.682729966

Reorder the terms:
3.25 + u = -3.682729966

Solving
3.25 + u = -3.682729966

Solving for variable 'u'.

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

Add '-3.25' to each side of the equation.
3.25 + -3.25 + u = -3.682729966 + -3.25

Combine like terms: 3.25 + -3.25 = 0.00
0.00 + u = -3.682729966 + -3.25
u = -3.682729966 + -3.25

Combine like terms: -3.682729966 + -3.25 = -6.932729966
u = -6.932729966

Simplifying
u = -6.932729966

Solution
The solution to the problem is based on the solutions
from the subproblems.
u = {0.432729966, -6.932729966}
Solution
u = {0.432729966, -6.932729966}