-3u^2-48u=-111

Solution for -3u^2-48u=-111 equation:

Simplifying
-3u2 + -48u = -111

Reorder the terms:
-48u + -3u2 = -111

Solving
-48u + -3u2 = -111

Solving for variable 'u'.

Reorder the terms:
111 + -48u + -3u2 = -111 + 111

Combine like terms: -111 + 111 = 0
111 + -48u + -3u2 = 0

Factor out the Greatest Common Factor (GCF), '3'.
3(37 + -16u + -1u2) = 0

Ignore the factor 3.
Subproblem 1
Set the factor '(37 + -16u + -1u2)' equal to zero and attempt to solve:

Simplifying
37 + -16u + -1u2 = 0

Solving
37 + -16u + -1u2 = 0

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

Divide each side by '-1'.
-37 + 16u + u2 = 0

Move the constant term to the right:

Add '37' to each side of the equation.
-37 + 16u + 37 + u2 = 0 + 37

Reorder the terms:
-37 + 37 + 16u + u2 = 0 + 37

Combine like terms: -37 + 37 = 0
0 + 16u + u2 = 0 + 37
16u + u2 = 0 + 37

Combine like terms: 0 + 37 = 37
16u + u2 = 37

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 = 37 + 64

Reorder the terms:
64 + 16u + u2 = 37 + 64

Combine like terms: 37 + 64 = 101
64 + 16u + u2 = 101

Factor a perfect square on the left side:
(u + 8)(u + 8) = 101

Calculate the square root of the right side: 10.049875621

Break this problem into two subproblems by setting 
(u + 8) equal to 10.049875621 and -10.049875621.

Subproblem 1
u + 8 = 10.049875621

Simplifying
u + 8 = 10.049875621

Reorder the terms:
8 + u = 10.049875621

Solving
8 + u = 10.049875621

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 = 10.049875621 + -8

Combine like terms: 8 + -8 = 0
0 + u = 10.049875621 + -8
u = 10.049875621 + -8

Combine like terms: 10.049875621 + -8 = 2.049875621
u = 2.049875621

Simplifying
u = 2.049875621

Subproblem 2
u + 8 = -10.049875621

Simplifying
u + 8 = -10.049875621

Reorder the terms:
8 + u = -10.049875621

Solving
8 + u = -10.049875621

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 = -10.049875621 + -8

Combine like terms: 8 + -8 = 0
0 + u = -10.049875621 + -8
u = -10.049875621 + -8

Combine like terms: -10.049875621 + -8 = -18.049875621
u = -18.049875621

Simplifying
u = -18.049875621

Solution
The solution to the problem is based on the solutions
from the subproblems.
u = {2.049875621, -18.049875621}
Solution
u = {2.049875621, -18.049875621}