5a^2+8a+3=0

Solution for 5a^2+8a+3=0 equation:

Simplifying
5a2 + 8a + 3 = 0

Reorder the terms:
3 + 8a + 5a2 = 0

Solving
3 + 8a + 5a2 = 0

Solving for variable 'a'.

Factor a trinomial.
(1 + a)(3 + 5a) = 0

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

Simplifying
1 + a = 0

Solving
1 + a = 0

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

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

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

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

Simplifying
a = -1
Subproblem 2
Set the factor '(3 + 5a)' equal to zero and attempt to solve:

Simplifying
3 + 5a = 0

Solving
3 + 5a = 0

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

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

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

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

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

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