a^2=27-6a

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

Simplifying
a2 = 27 + -6a

Solving
a2 = 27 + -6a

Solving for variable 'a'.

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

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

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

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

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

Subproblem 1
Set the factor '(-9 + -1a)' equal to zero and attempt to solve:

Simplifying
-9 + -1a = 0

Solving
-9 + -1a = 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 + -1a = 0 + 9

Combine like terms: -9 + 9 = 0
0 + -1a = 0 + 9
-1a = 0 + 9

Combine like terms: 0 + 9 = 9
-1a = 9

Divide each side by '-1'.
a = -9

Simplifying
a = -9
Subproblem 2
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
Solution
a = {-9, 3}