2u^2-12u+22-u^2+2u-1=0

Solution for 2u^2-12u+22-u^2+2u-1=0 equation:

Simplifying
2u2 + -12u + 22 + -1u2 + 2u + -1 = 0

Reorder the terms:
22 + -1 + -12u + 2u + 2u2 + -1u2 = 0

Combine like terms: 22 + -1 = 21
21 + -12u + 2u + 2u2 + -1u2 = 0

Combine like terms: -12u + 2u = -10u
21 + -10u + 2u2 + -1u2 = 0

Combine like terms: 2u2 + -1u2 = 1u2
21 + -10u + 1u2 = 0

Solving
21 + -10u + 1u2 = 0

Solving for variable 'u'.

Factor a trinomial.
(3 + -1u)(7 + -1u) = 0

Subproblem 1
Set the factor '(3 + -1u)' equal to zero and attempt to solve:

Simplifying
3 + -1u = 0

Solving
3 + -1u = 0

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

Add '-3' to each side of the equation.
3 + -3 + -1u = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -1u = 0 + -3
-1u = 0 + -3

Combine like terms: 0 + -3 = -3
-1u = -3

Divide each side by '-1'.
u = 3

Simplifying
u = 3
Subproblem 2
Set the factor '(7 + -1u)' equal to zero and attempt to solve:

Simplifying
7 + -1u = 0

Solving
7 + -1u = 0

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

Add '-7' to each side of the equation.
7 + -7 + -1u = 0 + -7

Combine like terms: 7 + -7 = 0
0 + -1u = 0 + -7
-1u = 0 + -7

Combine like terms: 0 + -7 = -7
-1u = -7

Divide each side by '-1'.
u = 7

Simplifying
u = 7
Solution
u = {3, 7}