a^2+2a+3a+6=

Solution for a^2+2a+3a+6= equation:

Simplifying
a2 + 2a + 3a + 6 = 0

Reorder the terms:
6 + 2a + 3a + a2 = 0

Combine like terms: 2a + 3a = 5a
6 + 5a + a2 = 0

Solving
6 + 5a + a2 = 0

Solving for variable 'a'.

Factor a trinomial.
(3 + a)(2 + a) = 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 '(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
Solution
a = {-3, -2}