a^2-3a=27+3a

Solution for a^2-3a=27+3a equation:

Simplifying
a2 + -3a = 27 + 3a

Reorder the terms:
-3a + a2 = 27 + 3a

Solving
-3a + a2 = 27 + 3a

Solving for variable 'a'.

Reorder the terms:
-27 + -3a + -3a + a2 = 27 + 3a + -27 + -3a

Combine like terms: -3a + -3a = -6a
-27 + -6a + a2 = 27 + 3a + -27 + -3a

Reorder the terms:
-27 + -6a + a2 = 27 + -27 + 3a + -3a

Combine like terms: 27 + -27 = 0
-27 + -6a + a2 = 0 + 3a + -3a
-27 + -6a + a2 = 3a + -3a

Combine like terms: 3a + -3a = 0
-27 + -6a + a2 = 0

Factor a trinomial.
(-3 + -1a)(9 + -1a) = 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 + -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
Solution
a = {-3, 9}