6a^2+15a+6=0

Solution for 6a^2+15a+6=0 equation:

Simplifying
6a2 + 15a + 6 = 0

Reorder the terms:
6 + 15a + 6a2 = 0

Solving
6 + 15a + 6a2 = 0

Solving for variable 'a'.

Factor out the Greatest Common Factor (GCF), '3'.
3(2 + 5a + 2a2) = 0

Factor a trinomial.
3((2 + a)(1 + 2a)) = 0

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

Simplifying
2 + a = 0

Solving
2 + a = 0

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

Add '-2' to each side of the equation.
2 + -2 + a = 0 + -2

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

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

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

Simplifying
1 + 2a = 0

Solving
1 + 2a = 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 + 2a = 0 + -1

Combine like terms: 1 + -1 = 0
0 + 2a = 0 + -1
2a = 0 + -1

Combine like terms: 0 + -1 = -1
2a = -1

Divide each side by '2'.
a = -0.5

Simplifying
a = -0.5
Solution
a = {-2, -0.5}