5a^2+19a+12=0

Solution for 5a^2+19a+12=0 equation:

Simplifying
5a2 + 19a + 12 = 0

Reorder the terms:
12 + 19a + 5a2 = 0

Solving
12 + 19a + 5a2 = 0

Solving for variable 'a'.

Factor a trinomial.
(3 + a)(4 + 5a) = 0

Subproblem 1
Set the factor '(3 + a)' equal to zero and attempt to solve:

Simplifying
3 + a = 0

Solving
3 + a = 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 + a = 0 + -3

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

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

Simplifying
a = -3
Subproblem 2
Set the factor '(4 + 5a)' equal to zero and attempt to solve:

Simplifying
4 + 5a = 0

Solving
4 + 5a = 0

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

Add '-4' to each side of the equation.
4 + -4 + 5a = 0 + -4

Combine like terms: 4 + -4 = 0
0 + 5a = 0 + -4
5a = 0 + -4

Combine like terms: 0 + -4 = -4
5a = -4

Divide each side by '5'.
a = -0.8

Simplifying
a = -0.8
Solution
a = {-3, -0.8}