2u^2-11u+3-u^2+6u-9=0

Solution for 2u^2-11u+3-u^2+6u-9=0 equation:

Simplifying
2u2 + -11u + 3 + -1u2 + 6u + -9 = 0

Reorder the terms:
3 + -9 + -11u + 6u + 2u2 + -1u2 = 0

Combine like terms: 3 + -9 = -6
-6 + -11u + 6u + 2u2 + -1u2 = 0

Combine like terms: -11u + 6u = -5u
-6 + -5u + 2u2 + -1u2 = 0

Combine like terms: 2u2 + -1u2 = 1u2
-6 + -5u + 1u2 = 0

Solving
-6 + -5u + 1u2 = 0

Solving for variable 'u'.

Factor a trinomial.
(-1 + -1u)(6 + -1u) = 0

Subproblem 1
Set the factor '(-1 + -1u)' equal to zero and attempt to solve:

Simplifying
-1 + -1u = 0

Solving
-1 + -1u = 0

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

Add '1' to each side of the equation.
-1 + 1 + -1u = 0 + 1

Combine like terms: -1 + 1 = 0
0 + -1u = 0 + 1
-1u = 0 + 1

Combine like terms: 0 + 1 = 1
-1u = 1

Divide each side by '-1'.
u = -1

Simplifying
u = -1
Subproblem 2
Set the factor '(6 + -1u)' equal to zero and attempt to solve:

Simplifying
6 + -1u = 0

Solving
6 + -1u = 0

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

Add '-6' to each side of the equation.
6 + -6 + -1u = 0 + -6

Combine like terms: 6 + -6 = 0
0 + -1u = 0 + -6
-1u = 0 + -6

Combine like terms: 0 + -6 = -6
-1u = -6

Divide each side by '-1'.
u = 6

Simplifying
u = 6
Solution
u = {-1, 6}