4u^2+48u-68=0

Solution for 4u^2+48u-68=0 equation:

Simplifying
4u2 + 48u + -68 = 0

Reorder the terms:
-68 + 48u + 4u2 = 0

Solving
-68 + 48u + 4u2 = 0

Solving for variable 'u'.

Factor out the Greatest Common Factor (GCF), '4'.
4(-17 + 12u + u2) = 0

Ignore the factor 4.
Subproblem 1
Set the factor '(-17 + 12u + u2)' equal to zero and attempt to solve:

Simplifying
-17 + 12u + u2 = 0

Solving
-17 + 12u + u2 = 0

Begin completing the square.

Move the constant term to the right:

Add '17' to each side of the equation.
-17 + 12u + 17 + u2 = 0 + 17

Reorder the terms:
-17 + 17 + 12u + u2 = 0 + 17

Combine like terms: -17 + 17 = 0
0 + 12u + u2 = 0 + 17
12u + u2 = 0 + 17

Combine like terms: 0 + 17 = 17
12u + u2 = 17

The u term is 12u.  Take half its coefficient (6).
Square it (36) and add it to both sides.

Add '36' to each side of the equation.
12u + 36 + u2 = 17 + 36

Reorder the terms:
36 + 12u + u2 = 17 + 36

Combine like terms: 17 + 36 = 53
36 + 12u + u2 = 53

Factor a perfect square on the left side:
(u + 6)(u + 6) = 53

Calculate the square root of the right side: 7.280109889

Break this problem into two subproblems by setting 
(u + 6) equal to 7.280109889 and -7.280109889.

Subproblem 1
u + 6 = 7.280109889

Simplifying
u + 6 = 7.280109889

Reorder the terms:
6 + u = 7.280109889

Solving
6 + u = 7.280109889

Solving for variable 'u'.

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

Add '-6' to each side of the equation.
6 + -6 + u = 7.280109889 + -6

Combine like terms: 6 + -6 = 0
0 + u = 7.280109889 + -6
u = 7.280109889 + -6

Combine like terms: 7.280109889 + -6 = 1.280109889
u = 1.280109889

Simplifying
u = 1.280109889

Subproblem 2
u + 6 = -7.280109889

Simplifying
u + 6 = -7.280109889

Reorder the terms:
6 + u = -7.280109889

Solving
6 + u = -7.280109889

Solving for variable 'u'.

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

Add '-6' to each side of the equation.
6 + -6 + u = -7.280109889 + -6

Combine like terms: 6 + -6 = 0
0 + u = -7.280109889 + -6
u = -7.280109889 + -6

Combine like terms: -7.280109889 + -6 = -13.280109889
u = -13.280109889

Simplifying
u = -13.280109889

Solution
The solution to the problem is based on the solutions
from the subproblems.
u = {1.280109889, -13.280109889}
Solution
u = {1.280109889, -13.280109889}