6a^2+17a+12=0

Solution for 6a^2+17a+12=0 equation:

Simplifying
6a2 + 17a + 12 = 0

Reorder the terms:
12 + 17a + 6a2 = 0

Solving
12 + 17a + 6a2 = 0

Solving for variable 'a'.

Factor a trinomial.
(3 + 2a)(4 + 3a) = 0

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

Simplifying
3 + 2a = 0

Solving
3 + 2a = 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 + 2a = 0 + -3

Combine like terms: 3 + -3 = 0
0 + 2a = 0 + -3
2a = 0 + -3

Combine like terms: 0 + -3 = -3
2a = -3

Divide each side by '2'.
a = -1.5

Simplifying
a = -1.5
Subproblem 2
Set the factor '(4 + 3a)' equal to zero and attempt to solve:

Simplifying
4 + 3a = 0

Solving
4 + 3a = 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 + 3a = 0 + -4

Combine like terms: 4 + -4 = 0
0 + 3a = 0 + -4
3a = 0 + -4

Combine like terms: 0 + -4 = -4
3a = -4

Divide each side by '3'.
a = -1.333333333

Simplifying
a = -1.333333333
Solution
a = {-1.5, -1.333333333}