8u^2+13u+5=0

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

Simplifying
8u2 + 13u + 5 = 0

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

Solving
5 + 13u + 8u2 = 0

Solving for variable 'u'.

Factor a trinomial.
(1 + u)(5 + 8u) = 0

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

Simplifying
1 + u = 0

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

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

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

Simplifying
u = -1
Subproblem 2
Set the factor '(5 + 8u)' equal to zero and attempt to solve:

Simplifying
5 + 8u = 0

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

Combine like terms: 5 + -5 = 0
0 + 8u = 0 + -5
8u = 0 + -5

Combine like terms: 0 + -5 = -5
8u = -5

Divide each side by '8'.
u = -0.625

Simplifying
u = -0.625
Solution
u = {-1, -0.625}