(2u^2-3u+6)+(-4u^2+u+5)=

Solution for (2u^2-3u+6)+(-4u^2+u+5)= equation:

Simplifying
(2u2 + -3u + 6) + (-4u2 + u + 5) = 0

Reorder the terms:
(6 + -3u + 2u2) + (-4u2 + u + 5) = 0

Remove parenthesis around (6 + -3u + 2u2)
6 + -3u + 2u2 + (-4u2 + u + 5) = 0

Reorder the terms:
6 + -3u + 2u2 + (5 + u + -4u2) = 0

Remove parenthesis around (5 + u + -4u2)
6 + -3u + 2u2 + 5 + u + -4u2 = 0

Reorder the terms:
6 + 5 + -3u + u + 2u2 + -4u2 = 0

Combine like terms: 6 + 5 = 11
11 + -3u + u + 2u2 + -4u2 = 0

Combine like terms: -3u + u = -2u
11 + -2u + 2u2 + -4u2 = 0

Combine like terms: 2u2 + -4u2 = -2u2
11 + -2u + -2u2 = 0

Solving
11 + -2u + -2u2 = 0

Solving for variable 'u'.

Begin completing the square.  Divide all terms by
-2 the coefficient of the squared term: 

Divide each side by '-2'.
-5.5 + u + u2 = 0

Move the constant term to the right:

Add '5.5' to each side of the equation.
-5.5 + u + 5.5 + u2 = 0 + 5.5

Reorder the terms:
-5.5 + 5.5 + u + u2 = 0 + 5.5

Combine like terms: -5.5 + 5.5 = 0.0
0.0 + u + u2 = 0 + 5.5
u + u2 = 0 + 5.5

Combine like terms: 0 + 5.5 = 5.5
u + u2 = 5.5

The u term is u.  Take half its coefficient (0.5).
Square it (0.25) and add it to both sides.

Add '0.25' to each side of the equation.
 + 0.25 + u2 = 5.5 + 0.25

Combine like terms:  + 0.25 = 1.25
1.25 + u2 = 5.5 + 0.25

Combine like terms: 5.5 + 0.25 = 5.75
1.25 + u2 = 5.75

Factor a perfect square on the left side:
(u + 0.5)(u + 0.5) = 5.75

Calculate the square root of the right side: 2.397915762

Break this problem into two subproblems by setting 
(u + 0.5) equal to 2.397915762 and -2.397915762.

Subproblem 1
u + 0.5 = 2.397915762

Simplifying
u + 0.5 = 2.397915762

Reorder the terms:
0.5 + u = 2.397915762

Solving
0.5 + u = 2.397915762

Solving for variable 'u'.

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

Add '-0.5' to each side of the equation.
0.5 + -0.5 + u = 2.397915762 + -0.5

Combine like terms: 0.5 + -0.5 = 0.0
0.0 + u = 2.397915762 + -0.5
u = 2.397915762 + -0.5

Combine like terms: 2.397915762 + -0.5 = 1.897915762
u = 1.897915762

Simplifying
u = 1.897915762

Subproblem 2
u + 0.5 = -2.397915762

Simplifying
u + 0.5 = -2.397915762

Reorder the terms:
0.5 + u = -2.397915762

Solving
0.5 + u = -2.397915762

Solving for variable 'u'.

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

Add '-0.5' to each side of the equation.
0.5 + -0.5 + u = -2.397915762 + -0.5

Combine like terms: 0.5 + -0.5 = 0.0
0.0 + u = -2.397915762 + -0.5
u = -2.397915762 + -0.5

Combine like terms: -2.397915762 + -0.5 = -2.897915762
u = -2.897915762

Simplifying
u = -2.897915762

Solution
The solution to the problem is based on the solutions
from the subproblems.
u = {1.897915762, -2.897915762}