a^2+3a=-2

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

Simplifying
a2 + 3a = -2

Reorder the terms:
3a + a2 = -2

Solving
3a + a2 = -2

Solving for variable 'a'.

Reorder the terms:
2 + 3a + a2 = -2 + 2

Combine like terms: -2 + 2 = 0
2 + 3a + a2 = 0

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

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 + 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
Solution
a = {-2, -1}