q^2-12q+11=0

Solution for q^2-12q+11=0 equation:

Simplifying
q2 + -12q + 11 = 0

Reorder the terms:
11 + -12q + q2 = 0

Solving
11 + -12q + q2 = 0

Solving for variable 'q'.

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

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

Simplifying
1 + -1q = 0

Solving
1 + -1q = 0

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

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

Combine like terms: 1 + -1 = 0
0 + -1q = 0 + -1
-1q = 0 + -1

Combine like terms: 0 + -1 = -1
-1q = -1

Divide each side by '-1'.
q = 1

Simplifying
q = 1
Subproblem 2
Set the factor '(11 + -1q)' equal to zero and attempt to solve:

Simplifying
11 + -1q = 0

Solving
11 + -1q = 0

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

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

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

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

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

Simplifying
q = 11
Solution
q = {1, 11}