5u^2-8u-13=0

Solution for 5u^2-8u-13=0 equation:

Simplifying
5u2 + -8u + -13 = 0

Reorder the terms:
-13 + -8u + 5u2 = 0

Solving
-13 + -8u + 5u2 = 0

Solving for variable 'u'.

Factor a trinomial.
(-1 + -1u)(13 + -5u) = 0

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

Simplifying
-1 + -1u = 0

Solving
-1 + -1u = 0

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

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

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

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

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

Simplifying
u = -1
Subproblem 2
Set the factor '(13 + -5u)' equal to zero and attempt to solve:

Simplifying
13 + -5u = 0

Solving
13 + -5u = 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 + -5u = 0 + -13

Combine like terms: 13 + -13 = 0
0 + -5u = 0 + -13
-5u = 0 + -13

Combine like terms: 0 + -13 = -13
-5u = -13

Divide each side by '-5'.
u = 2.6

Simplifying
u = 2.6
Solution
u = {-1, 2.6}