a^2+9a=-14

Solution for a^2+9a=-14 equation:

Simplifying
a2 + 9a = -14

Reorder the terms:
9a + a2 = -14

Solving
9a + a2 = -14

Solving for variable 'a'.

Reorder the terms:
14 + 9a + a2 = -14 + 14

Combine like terms: -14 + 14 = 0
14 + 9a + a2 = 0

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

Subproblem 1
Set the factor '(7 + a)' equal to zero and attempt to solve:

Simplifying
7 + a = 0

Solving
7 + a = 0

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

Add '-7' to each side of the equation.
7 + -7 + a = 0 + -7

Combine like terms: 7 + -7 = 0
0 + a = 0 + -7
a = 0 + -7

Combine like terms: 0 + -7 = -7
a = -7

Simplifying
a = -7
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 = {-7, -2}