a^2-9a+11=-7

Solution for a^2-9a+11=-7 equation:

Simplifying
a2 + -9a + 11 = -7

Reorder the terms:
11 + -9a + a2 = -7

Solving
11 + -9a + a2 = -7

Solving for variable 'a'.

Reorder the terms:
11 + 7 + -9a + a2 = -7 + 7

Combine like terms: 11 + 7 = 18
18 + -9a + a2 = -7 + 7

Combine like terms: -7 + 7 = 0
18 + -9a + 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}