a^2=3a+18

Solution for a^2=3a+18 equation:

Simplifying
a2 = 3a + 18

Reorder the terms:
a2 = 18 + 3a

Solving
a2 = 18 + 3a

Solving for variable 'a'.

Reorder the terms:
-18 + -3a + a2 = 18 + 3a + -18 + -3a

Reorder the terms:
-18 + -3a + a2 = 18 + -18 + 3a + -3a

Combine like terms: 18 + -18 = 0
-18 + -3a + a2 = 0 + 3a + -3a
-18 + -3a + a2 = 3a + -3a

Combine like terms: 3a + -3a = 0
-18 + -3a + a2 = 0

Factor a trinomial.
(-3 + -1a)(6 + -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 '(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
Solution
a = {-3, 6}