-a^2+9a=-22

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

Simplifying
-1a2 + 9a = -22

Reorder the terms:
9a + -1a2 = -22

Solving
9a + -1a2 = -22

Solving for variable 'a'.

Reorder the terms:
22 + 9a + -1a2 = -22 + 22

Combine like terms: -22 + 22 = 0
22 + 9a + -1a2 = 0

Factor a trinomial.
(11 + -1a)(2 + a) = 0

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

Simplifying
2 + a = 0

Solving
2 + a = 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 + a = 0 + -2

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

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

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