0=u^2+5u-24

Solution for 0=u^2+5u-24 equation:

Simplifying
0 = u2 + 5u + -24

Reorder the terms:
0 = -24 + 5u + u2

Solving
0 = -24 + 5u + u2

Solving for variable 'u'.

Combine like terms: 0 + 24 = 24
24 + -5u + -1u2 = -24 + 5u + u2 + 24 + -5u + -1u2

Reorder the terms:
24 + -5u + -1u2 = -24 + 24 + 5u + -5u + u2 + -1u2

Combine like terms: -24 + 24 = 0
24 + -5u + -1u2 = 0 + 5u + -5u + u2 + -1u2
24 + -5u + -1u2 = 5u + -5u + u2 + -1u2

Combine like terms: 5u + -5u = 0
24 + -5u + -1u2 = 0 + u2 + -1u2
24 + -5u + -1u2 = u2 + -1u2

Combine like terms: u2 + -1u2 = 0
24 + -5u + -1u2 = 0

Factor a trinomial.
(3 + -1u)(8 + 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 '(8 + u)' equal to zero and attempt to solve:

Simplifying
8 + u = 0

Solving
8 + u = 0

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

Add '-8' to each side of the equation.
8 + -8 + u = 0 + -8

Combine like terms: 8 + -8 = 0
0 + u = 0 + -8
u = 0 + -8

Combine like terms: 0 + -8 = -8
u = -8

Simplifying
u = -8
Solution
u = {3, -8}