0=u^2-u-6

Solution for 0=u^2-u-6 equation:

Simplifying
0 = u2 + -1u + -6

Reorder the terms:
0 = -6 + -1u + u2

Solving
0 = -6 + -1u + u2

Solving for variable 'u'.

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

Reorder the terms:
6 + u + -1u2 = -6 + 6 + -1u + u + u2 + -1u2

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

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

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

Factor a trinomial.
(3 + -1u)(2 + u) = 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 '(2 + u)' equal to zero and attempt to solve:

Simplifying
2 + u = 0

Solving
2 + u = 0

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

Add '-2' to each side of the equation.
2 + -2 + u = 0 + -2

Combine like terms: 2 + -2 = 0
0 + u = 0 + -2
u = 0 + -2

Combine like terms: 0 + -2 = -2
u = -2

Simplifying
u = -2
Solution
u = {3, -2}