5u^2+8u=-3

Solution for 5u^2+8u=-3 equation:

Simplifying
5u2 + 8u = -3

Reorder the terms:
8u + 5u2 = -3

Solving
8u + 5u2 = -3

Solving for variable 'u'.

Reorder the terms:
3 + 8u + 5u2 = -3 + 3

Combine like terms: -3 + 3 = 0
3 + 8u + 5u2 = 0

Factor a trinomial.
(1 + u)(3 + 5u) = 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 '(3 + 5u)' equal to zero and attempt to solve:

Simplifying
3 + 5u = 0

Solving
3 + 5u = 0

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

Add '-3' to each side of the equation.
3 + -3 + 5u = 0 + -3

Combine like terms: 3 + -3 = 0
0 + 5u = 0 + -3
5u = 0 + -3

Combine like terms: 0 + -3 = -3
5u = -3

Divide each side by '5'.
u = -0.6

Simplifying
u = -0.6
Solution
u = {-1, -0.6}