a^2+9a-27=8a+3

Solution for a^2+9a-27=8a+3 equation:

Simplifying
a2 + 9a + -27 = 8a + 3

Reorder the terms:
-27 + 9a + a2 = 8a + 3

Reorder the terms:
-27 + 9a + a2 = 3 + 8a

Solving
-27 + 9a + a2 = 3 + 8a

Solving for variable 'a'.

Reorder the terms:
-27 + -3 + 9a + -8a + a2 = 3 + 8a + -3 + -8a

Combine like terms: -27 + -3 = -30
-30 + 9a + -8a + a2 = 3 + 8a + -3 + -8a

Combine like terms: 9a + -8a = 1a
-30 + 1a + a2 = 3 + 8a + -3 + -8a

Reorder the terms:
-30 + 1a + a2 = 3 + -3 + 8a + -8a

Combine like terms: 3 + -3 = 0
-30 + 1a + a2 = 0 + 8a + -8a
-30 + 1a + a2 = 8a + -8a

Combine like terms: 8a + -8a = 0
-30 + 1a + a2 = 0

Factor a trinomial.
(-6 + -1a)(5 + -1a) = 0

Subproblem 1
Set the factor '(-6 + -1a)' equal to zero and attempt to solve:

Simplifying
-6 + -1a = 0

Solving
-6 + -1a = 0

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

Add '6' to each side of the equation.
-6 + 6 + -1a = 0 + 6

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

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

Divide each side by '-1'.
a = -6

Simplifying
a = -6
Subproblem 2
Set the factor '(5 + -1a)' equal to zero and attempt to solve:

Simplifying
5 + -1a = 0

Solving
5 + -1a = 0

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

Add '-5' to each side of the equation.
5 + -5 + -1a = 0 + -5

Combine like terms: 5 + -5 = 0
0 + -1a = 0 + -5
-1a = 0 + -5

Combine like terms: 0 + -5 = -5
-1a = -5

Divide each side by '-1'.
a = 5

Simplifying
a = 5
Solution
a = {-6, 5}