-12u-5=-4u^2

Solution for -12u-5=-4u^2 equation:

Simplifying
-12u + -5 = -4u2

Reorder the terms:
-5 + -12u = -4u2

Solving
-5 + -12u = -4u2

Solving for variable 'u'.

Combine like terms: -4u2 + 4u2 = 0
-5 + -12u + 4u2 = 0

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

Divide each side by '4'.
-1.25 + -3u + u2 = 0

Move the constant term to the right:

Add '1.25' to each side of the equation.
-1.25 + -3u + 1.25 + u2 = 0 + 1.25

Reorder the terms:
-1.25 + 1.25 + -3u + u2 = 0 + 1.25

Combine like terms: -1.25 + 1.25 = 0.00
0.00 + -3u + u2 = 0 + 1.25
-3u + u2 = 0 + 1.25

Combine like terms: 0 + 1.25 = 1.25
-3u + u2 = 1.25

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 = 1.25 + 2.25

Reorder the terms:
2.25 + -3u + u2 = 1.25 + 2.25

Combine like terms: 1.25 + 2.25 = 3.5
2.25 + -3u + u2 = 3.5

Factor a perfect square on the left side:
(u + -1.5)(u + -1.5) = 3.5

Calculate the square root of the right side: 1.870828693

Break this problem into two subproblems by setting 
(u + -1.5) equal to 1.870828693 and -1.870828693.

Subproblem 1
u + -1.5 = 1.870828693

Simplifying
u + -1.5 = 1.870828693

Reorder the terms:
-1.5 + u = 1.870828693

Solving
-1.5 + u = 1.870828693

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 = 1.870828693 + 1.5

Combine like terms: -1.5 + 1.5 = 0.0
0.0 + u = 1.870828693 + 1.5
u = 1.870828693 + 1.5

Combine like terms: 1.870828693 + 1.5 = 3.370828693
u = 3.370828693

Simplifying
u = 3.370828693

Subproblem 2
u + -1.5 = -1.870828693

Simplifying
u + -1.5 = -1.870828693

Reorder the terms:
-1.5 + u = -1.870828693

Solving
-1.5 + u = -1.870828693

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 = -1.870828693 + 1.5

Combine like terms: -1.5 + 1.5 = 0.0
0.0 + u = -1.870828693 + 1.5
u = -1.870828693 + 1.5

Combine like terms: -1.870828693 + 1.5 = -0.370828693
u = -0.370828693

Simplifying
u = -0.370828693

Solution
The solution to the problem is based on the solutions
from the subproblems.
u = {3.370828693, -0.370828693}