u^2+9u-52=0

Solution for u^2+9u-52=0 equation:

Simplifying
u2 + 9u + -52 = 0

Reorder the terms:
-52 + 9u + u2 = 0

Solving
-52 + 9u + u2 = 0

Solving for variable 'u'.

Factor a trinomial.
(-13 + -1u)(4 + -1u) = 0

Subproblem 1
Set the factor '(-13 + -1u)' equal to zero and attempt to solve:

Simplifying
-13 + -1u = 0

Solving
-13 + -1u = 0

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

Add '13' to each side of the equation.
-13 + 13 + -1u = 0 + 13

Combine like terms: -13 + 13 = 0
0 + -1u = 0 + 13
-1u = 0 + 13

Combine like terms: 0 + 13 = 13
-1u = 13

Divide each side by '-1'.
u = -13

Simplifying
u = -13
Subproblem 2
Set the factor '(4 + -1u)' equal to zero and attempt to solve:

Simplifying
4 + -1u = 0

Solving
4 + -1u = 0

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

Add '-4' to each side of the equation.
4 + -4 + -1u = 0 + -4

Combine like terms: 4 + -4 = 0
0 + -1u = 0 + -4
-1u = 0 + -4

Combine like terms: 0 + -4 = -4
-1u = -4

Divide each side by '-1'.
u = 4

Simplifying
u = 4
Solution
u = {-13, 4}