0=a^2+6a-27

Solution for 0=a^2+6a-27 equation:

Simplifying
0 = a2 + 6a + -27

Reorder the terms:
0 = -27 + 6a + a2

Solving
0 = -27 + 6a + a2

Solving for variable 'a'.

Combine like terms: 0 + 27 = 27
27 + -6a + -1a2 = -27 + 6a + a2 + 27 + -6a + -1a2

Reorder the terms:
27 + -6a + -1a2 = -27 + 27 + 6a + -6a + a2 + -1a2

Combine like terms: -27 + 27 = 0
27 + -6a + -1a2 = 0 + 6a + -6a + a2 + -1a2
27 + -6a + -1a2 = 6a + -6a + a2 + -1a2

Combine like terms: 6a + -6a = 0
27 + -6a + -1a2 = 0 + a2 + -1a2
27 + -6a + -1a2 = a2 + -1a2

Combine like terms: a2 + -1a2 = 0
27 + -6a + -1a2 = 0

Factor a trinomial.
(3 + -1a)(9 + a) = 0

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

Simplifying
3 + -1a = 0

Solving
3 + -1a = 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 + -1a = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -1a = 0 + -3
-1a = 0 + -3

Combine like terms: 0 + -3 = -3
-1a = -3

Divide each side by '-1'.
a = 3

Simplifying
a = 3
Subproblem 2
Set the factor '(9 + a)' equal to zero and attempt to solve:

Simplifying
9 + a = 0

Solving
9 + a = 0

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

Add '-9' to each side of the equation.
9 + -9 + a = 0 + -9

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

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

Simplifying
a = -9
Solution
a = {3, -9}