a^2=11a-18

Solution for a^2=11a-18 equation:

Simplifying
a2 = 11a + -18

Reorder the terms:
a2 = -18 + 11a

Solving
a2 = -18 + 11a

Solving for variable 'a'.

Reorder the terms:
18 + -11a + a2 = -18 + 11a + 18 + -11a

Reorder the terms:
18 + -11a + a2 = -18 + 18 + 11a + -11a

Combine like terms: -18 + 18 = 0
18 + -11a + a2 = 0 + 11a + -11a
18 + -11a + a2 = 11a + -11a

Combine like terms: 11a + -11a = 0
18 + -11a + a2 = 0

Factor a trinomial.
(2 + -1a)(9 + -1a) = 0

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

Simplifying
2 + -1a = 0

Solving
2 + -1a = 0

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

Add '-2' to each side of the equation.
2 + -2 + -1a = 0 + -2

Combine like terms: 2 + -2 = 0
0 + -1a = 0 + -2
-1a = 0 + -2

Combine like terms: 0 + -2 = -2
-1a = -2

Divide each side by '-1'.
a = 2

Simplifying
a = 2
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 = {2, 9}