u^2=3u+10

Solution for u^2=3u+10 equation:

Simplifying
u2 = 3u + 10

Reorder the terms:
u2 = 10 + 3u

Solving
u2 = 10 + 3u

Solving for variable 'u'.

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

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

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

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

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

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

Simplifying
-2 + -1u = 0

Solving
-2 + -1u = 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 + -1u = 0 + 2

Combine like terms: -2 + 2 = 0
0 + -1u = 0 + 2
-1u = 0 + 2

Combine like terms: 0 + 2 = 2
-1u = 2

Divide each side by '-1'.
u = -2

Simplifying
u = -2
Subproblem 2
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
Solution
u = {-2, 5}