-3u^2-18u+75=0

Solution for -3u^2-18u+75=0 equation:

Simplifying
-3u2 + -18u + 75 = 0

Reorder the terms:
75 + -18u + -3u2 = 0

Solving
75 + -18u + -3u2 = 0

Solving for variable 'u'.

Factor out the Greatest Common Factor (GCF), '3'.
3(25 + -6u + -1u2) = 0

Ignore the factor 3.
Subproblem 1
Set the factor '(25 + -6u + -1u2)' equal to zero and attempt to solve:

Simplifying
25 + -6u + -1u2 = 0

Solving
25 + -6u + -1u2 = 0

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

Divide each side by '-1'.
-25 + 6u + u2 = 0

Move the constant term to the right:

Add '25' to each side of the equation.
-25 + 6u + 25 + u2 = 0 + 25

Reorder the terms:
-25 + 25 + 6u + u2 = 0 + 25

Combine like terms: -25 + 25 = 0
0 + 6u + u2 = 0 + 25
6u + u2 = 0 + 25

Combine like terms: 0 + 25 = 25
6u + u2 = 25

The u term is 6u.  Take half its coefficient (3).
Square it (9) and add it to both sides.

Add '9' to each side of the equation.
6u + 9 + u2 = 25 + 9

Reorder the terms:
9 + 6u + u2 = 25 + 9

Combine like terms: 25 + 9 = 34
9 + 6u + u2 = 34

Factor a perfect square on the left side:
(u + 3)(u + 3) = 34

Calculate the square root of the right side: 5.830951895

Break this problem into two subproblems by setting 
(u + 3) equal to 5.830951895 and -5.830951895.

Subproblem 1
u + 3 = 5.830951895

Simplifying
u + 3 = 5.830951895

Reorder the terms:
3 + u = 5.830951895

Solving
3 + u = 5.830951895

Solving for variable 'u'.

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

Add '-3' to each side of the equation.
3 + -3 + u = 5.830951895 + -3

Combine like terms: 3 + -3 = 0
0 + u = 5.830951895 + -3
u = 5.830951895 + -3

Combine like terms: 5.830951895 + -3 = 2.830951895
u = 2.830951895

Simplifying
u = 2.830951895

Subproblem 2
u + 3 = -5.830951895

Simplifying
u + 3 = -5.830951895

Reorder the terms:
3 + u = -5.830951895

Solving
3 + u = -5.830951895

Solving for variable 'u'.

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

Add '-3' to each side of the equation.
3 + -3 + u = -5.830951895 + -3

Combine like terms: 3 + -3 = 0
0 + u = -5.830951895 + -3
u = -5.830951895 + -3

Combine like terms: -5.830951895 + -3 = -8.830951895
u = -8.830951895

Simplifying
u = -8.830951895

Solution
The solution to the problem is based on the solutions
from the subproblems.
u = {2.830951895, -8.830951895}
Solution
u = {2.830951895, -8.830951895}