(q-2)(q-6)=5

Solution for (q-2)(q-6)=5 equation:

Simplifying
(q + -2)(q + -6) = 5

Reorder the terms:
(-2 + q)(q + -6) = 5

Reorder the terms:
(-2 + q)(-6 + q) = 5

Multiply (-2 + q) * (-6 + q)
(-2(-6 + q) + q(-6 + q)) = 5
((-6 * -2 + q * -2) + q(-6 + q)) = 5
((12 + -2q) + q(-6 + q)) = 5
(12 + -2q + (-6 * q + q * q)) = 5
(12 + -2q + (-6q + q2)) = 5

Combine like terms: -2q + -6q = -8q
(12 + -8q + q2) = 5

Solving
12 + -8q + q2 = 5

Solving for variable 'q'.

Reorder the terms:
12 + -5 + -8q + q2 = 5 + -5

Combine like terms: 12 + -5 = 7
7 + -8q + q2 = 5 + -5

Combine like terms: 5 + -5 = 0
7 + -8q + q2 = 0

Factor a trinomial.
(1 + -1q)(7 + -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 '(7 + -1q)' equal to zero and attempt to solve:

Simplifying
7 + -1q = 0

Solving
7 + -1q = 0

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

Add '-7' to each side of the equation.
7 + -7 + -1q = 0 + -7

Combine like terms: 7 + -7 = 0
0 + -1q = 0 + -7
-1q = 0 + -7

Combine like terms: 0 + -7 = -7
-1q = -7

Divide each side by '-1'.
q = 7

Simplifying
q = 7
Solution
q = {1, 7}