u^2-3u-12=0

Solution for u^2-3u-12=0 equation:

Simplifying
u2 + -3u + -12 = 0

Reorder the terms:
-12 + -3u + u2 = 0

Solving
-12 + -3u + u2 = 0

Solving for variable 'u'.

Begin completing the square.

Move the constant term to the right:

Add '12' to each side of the equation.
-12 + -3u + 12 + u2 = 0 + 12

Reorder the terms:
-12 + 12 + -3u + u2 = 0 + 12

Combine like terms: -12 + 12 = 0
0 + -3u + u2 = 0 + 12
-3u + u2 = 0 + 12

Combine like terms: 0 + 12 = 12
-3u + u2 = 12

The u term is -3u.  Take half its coefficient (-1.5).
Square it (2.25) and add it to both sides.

Add '2.25' to each side of the equation.
-3u + 2.25 + u2 = 12 + 2.25

Reorder the terms:
2.25 + -3u + u2 = 12 + 2.25

Combine like terms: 12 + 2.25 = 14.25
2.25 + -3u + u2 = 14.25

Factor a perfect square on the left side:
(u + -1.5)(u + -1.5) = 14.25

Calculate the square root of the right side: 3.774917218

Break this problem into two subproblems by setting 
(u + -1.5) equal to 3.774917218 and -3.774917218.

Subproblem 1
u + -1.5 = 3.774917218

Simplifying
u + -1.5 = 3.774917218

Reorder the terms:
-1.5 + u = 3.774917218

Solving
-1.5 + u = 3.774917218

Solving for variable 'u'.

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

Add '1.5' to each side of the equation.
-1.5 + 1.5 + u = 3.774917218 + 1.5

Combine like terms: -1.5 + 1.5 = 0.0
0.0 + u = 3.774917218 + 1.5
u = 3.774917218 + 1.5

Combine like terms: 3.774917218 + 1.5 = 5.274917218
u = 5.274917218

Simplifying
u = 5.274917218

Subproblem 2
u + -1.5 = -3.774917218

Simplifying
u + -1.5 = -3.774917218

Reorder the terms:
-1.5 + u = -3.774917218

Solving
-1.5 + u = -3.774917218

Solving for variable 'u'.

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

Add '1.5' to each side of the equation.
-1.5 + 1.5 + u = -3.774917218 + 1.5

Combine like terms: -1.5 + 1.5 = 0.0
0.0 + u = -3.774917218 + 1.5
u = -3.774917218 + 1.5

Combine like terms: -3.774917218 + 1.5 = -2.274917218
u = -2.274917218

Simplifying
u = -2.274917218

Solution
The solution to the problem is based on the solutions
from the subproblems.
u = {5.274917218, -2.274917218}