-5u^4(-7u^2+4u+9)=0

Solution for -5u^4(-7u^2+4u+9)=0 equation:

Simplifying
-5u4(-7u2 + 4u + 9) = 0

Reorder the terms:
-5u4(9 + 4u + -7u2) = 0
(9 * -5u4 + 4u * -5u4 + -7u2 * -5u4) = 0
(-45u4 + -20u5 + 35u6) = 0

Solving
-45u4 + -20u5 + 35u6 = 0

Solving for variable 'u'.

Factor out the Greatest Common Factor (GCF), '5u4'.
5u4(-9 + -4u + 7u2) = 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 '(-9 + -4u + 7u2)' equal to zero and attempt to solve:

Simplifying
-9 + -4u + 7u2 = 0

Solving
-9 + -4u + 7u2 = 0

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

Divide each side by '7'.
-1.285714286 + -0.5714285714u + u2 = 0

Move the constant term to the right:

Add '1.285714286' to each side of the equation.
-1.285714286 + -0.5714285714u + 1.285714286 + u2 = 0 + 1.285714286

Reorder the terms:
-1.285714286 + 1.285714286 + -0.5714285714u + u2 = 0 + 1.285714286

Combine like terms: -1.285714286 + 1.285714286 = 0.000000000
0.000000000 + -0.5714285714u + u2 = 0 + 1.285714286
-0.5714285714u + u2 = 0 + 1.285714286

Combine like terms: 0 + 1.285714286 = 1.285714286
-0.5714285714u + u2 = 1.285714286

The u term is -0.5714285714u.  Take half its coefficient (-0.2857142857).
Square it (0.08163265305) and add it to both sides.

Add '0.08163265305' to each side of the equation.
-0.5714285714u + 0.08163265305 + u2 = 1.285714286 + 0.08163265305

Reorder the terms:
0.08163265305 + -0.5714285714u + u2 = 1.285714286 + 0.08163265305

Combine like terms: 1.285714286 + 0.08163265305 = 1.36734693905
0.08163265305 + -0.5714285714u + u2 = 1.36734693905

Factor a perfect square on the left side:
(u + -0.2857142857)(u + -0.2857142857) = 1.36734693905

Calculate the square root of the right side: 1.16933611

Break this problem into two subproblems by setting 
(u + -0.2857142857) equal to 1.16933611 and -1.16933611.

Subproblem 1
u + -0.2857142857 = 1.16933611

Simplifying
u + -0.2857142857 = 1.16933611

Reorder the terms:
-0.2857142857 + u = 1.16933611

Solving
-0.2857142857 + u = 1.16933611

Solving for variable 'u'.

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

Add '0.2857142857' to each side of the equation.
-0.2857142857 + 0.2857142857 + u = 1.16933611 + 0.2857142857

Combine like terms: -0.2857142857 + 0.2857142857 = 0.0000000000
0.0000000000 + u = 1.16933611 + 0.2857142857
u = 1.16933611 + 0.2857142857

Combine like terms: 1.16933611 + 0.2857142857 = 1.4550503957
u = 1.4550503957

Simplifying
u = 1.4550503957

Subproblem 2
u + -0.2857142857 = -1.16933611

Simplifying
u + -0.2857142857 = -1.16933611

Reorder the terms:
-0.2857142857 + u = -1.16933611

Solving
-0.2857142857 + u = -1.16933611

Solving for variable 'u'.

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

Add '0.2857142857' to each side of the equation.
-0.2857142857 + 0.2857142857 + u = -1.16933611 + 0.2857142857

Combine like terms: -0.2857142857 + 0.2857142857 = 0.0000000000
0.0000000000 + u = -1.16933611 + 0.2857142857
u = -1.16933611 + 0.2857142857

Combine like terms: -1.16933611 + 0.2857142857 = -0.8836218243
u = -0.8836218243

Simplifying
u = -0.8836218243

Solution
The solution to the problem is based on the solutions
from the subproblems.
u = {1.4550503957, -0.8836218243}
Solution
u = {1.4550503957, -0.8836218243}