a^2-9a=22

Solution for a^2-9a=22 equation:

Simplifying
a2 + -9a = 22

Reorder the terms:
-9a + a2 = 22

Solving
-9a + a2 = 22

Solving for variable 'a'.

Reorder the terms:
-22 + -9a + a2 = 22 + -22

Combine like terms: 22 + -22 = 0
-22 + -9a + a2 = 0

Factor a trinomial.
(-2 + -1a)(11 + -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 '(11 + -1a)' equal to zero and attempt to solve:

Simplifying
11 + -1a = 0

Solving
11 + -1a = 0

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

Add '-11' to each side of the equation.
11 + -11 + -1a = 0 + -11

Combine like terms: 11 + -11 = 0
0 + -1a = 0 + -11
-1a = 0 + -11

Combine like terms: 0 + -11 = -11
-1a = -11

Divide each side by '-1'.
a = 11

Simplifying
a = 11
Solution
a = {-2, 11}