-4u^2-64u+156=0

Solution for -4u^2-64u+156=0 equation:

Simplifying
-4u2 + -64u + 156 = 0

Reorder the terms:
156 + -64u + -4u2 = 0

Solving
156 + -64u + -4u2 = 0

Solving for variable 'u'.

Factor out the Greatest Common Factor (GCF), '4'.
4(39 + -16u + -1u2) = 0

Ignore the factor 4.
Subproblem 1
Set the factor '(39 + -16u + -1u2)' equal to zero and attempt to solve:

Simplifying
39 + -16u + -1u2 = 0

Solving
39 + -16u + -1u2 = 0

Begin completing the square.  Divide all terms by
-1 the coefficient of the squared term: 

Divide each side by '-1'.
-39 + 16u + u2 = 0

Move the constant term to the right:

Add '39' to each side of the equation.
-39 + 16u + 39 + u2 = 0 + 39

Reorder the terms:
-39 + 39 + 16u + u2 = 0 + 39

Combine like terms: -39 + 39 = 0
0 + 16u + u2 = 0 + 39
16u + u2 = 0 + 39

Combine like terms: 0 + 39 = 39
16u + u2 = 39

The u term is 16u.  Take half its coefficient (8).
Square it (64) and add it to both sides.

Add '64' to each side of the equation.
16u + 64 + u2 = 39 + 64

Reorder the terms:
64 + 16u + u2 = 39 + 64

Combine like terms: 39 + 64 = 103
64 + 16u + u2 = 103

Factor a perfect square on the left side:
(u + 8)(u + 8) = 103

Calculate the square root of the right side: 10.148891565

Break this problem into two subproblems by setting 
(u + 8) equal to 10.148891565 and -10.148891565.

Subproblem 1
u + 8 = 10.148891565

Simplifying
u + 8 = 10.148891565

Reorder the terms:
8 + u = 10.148891565

Solving
8 + u = 10.148891565

Solving for variable 'u'.

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

Add '-8' to each side of the equation.
8 + -8 + u = 10.148891565 + -8

Combine like terms: 8 + -8 = 0
0 + u = 10.148891565 + -8
u = 10.148891565 + -8

Combine like terms: 10.148891565 + -8 = 2.148891565
u = 2.148891565

Simplifying
u = 2.148891565

Subproblem 2
u + 8 = -10.148891565

Simplifying
u + 8 = -10.148891565

Reorder the terms:
8 + u = -10.148891565

Solving
8 + u = -10.148891565

Solving for variable 'u'.

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

Add '-8' to each side of the equation.
8 + -8 + u = -10.148891565 + -8

Combine like terms: 8 + -8 = 0
0 + u = -10.148891565 + -8
u = -10.148891565 + -8

Combine like terms: -10.148891565 + -8 = -18.148891565
u = -18.148891565

Simplifying
u = -18.148891565

Solution
The solution to the problem is based on the solutions
from the subproblems.
u = {2.148891565, -18.148891565}
Solution
u = {2.148891565, -18.148891565}