0=u^2-3u-10

Solution for 0=u^2-3u-10 equation:

Simplifying
0 = u2 + -3u + -10

Reorder the terms:
0 = -10 + -3u + u2

Solving
0 = -10 + -3u + u2

Solving for variable 'u'.

Combine like terms: 0 + 10 = 10
10 + 3u + -1u2 = -10 + -3u + u2 + 10 + 3u + -1u2

Reorder the terms:
10 + 3u + -1u2 = -10 + 10 + -3u + 3u + u2 + -1u2

Combine like terms: -10 + 10 = 0
10 + 3u + -1u2 = 0 + -3u + 3u + u2 + -1u2
10 + 3u + -1u2 = -3u + 3u + u2 + -1u2

Combine like terms: -3u + 3u = 0
10 + 3u + -1u2 = 0 + u2 + -1u2
10 + 3u + -1u2 = u2 + -1u2

Combine like terms: u2 + -1u2 = 0
10 + 3u + -1u2 = 0

Factor a trinomial.
(5 + -1u)(2 + u) = 0

Subproblem 1
Set the factor '(5 + -1u)' equal to zero and attempt to solve:

Simplifying
5 + -1u = 0

Solving
5 + -1u = 0

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

Add '-5' to each side of the equation.
5 + -5 + -1u = 0 + -5

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

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

Divide each side by '-1'.
u = 5

Simplifying
u = 5
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 = {5, -2}