(r-2)(r-6)=-3

Solution for (r-2)(r-6)=-3 equation:

Simplifying
(r + -2)(r + -6) = -3

Reorder the terms:
(-2 + r)(r + -6) = -3

Reorder the terms:
(-2 + r)(-6 + r) = -3

Multiply (-2 + r) * (-6 + r)
(-2(-6 + r) + r(-6 + r)) = -3
((-6 * -2 + r * -2) + r(-6 + r)) = -3
((12 + -2r) + r(-6 + r)) = -3
(12 + -2r + (-6 * r + r * r)) = -3
(12 + -2r + (-6r + r2)) = -3

Combine like terms: -2r + -6r = -8r
(12 + -8r + r2) = -3

Solving
12 + -8r + r2 = -3

Solving for variable 'r'.

Reorder the terms:
12 + 3 + -8r + r2 = -3 + 3

Combine like terms: 12 + 3 = 15
15 + -8r + r2 = -3 + 3

Combine like terms: -3 + 3 = 0
15 + -8r + r2 = 0

Factor a trinomial.
(3 + -1r)(5 + -1r) = 0

Subproblem 1
Set the factor '(3 + -1r)' equal to zero and attempt to solve:

Simplifying
3 + -1r = 0

Solving
3 + -1r = 0

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

Add '-3' to each side of the equation.
3 + -3 + -1r = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -1r = 0 + -3
-1r = 0 + -3

Combine like terms: 0 + -3 = -3
-1r = -3

Divide each side by '-1'.
r = 3

Simplifying
r = 3
Subproblem 2
Set the factor '(5 + -1r)' equal to zero and attempt to solve:

Simplifying
5 + -1r = 0

Solving
5 + -1r = 0

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

Add '-5' to each side of the equation.
5 + -5 + -1r = 0 + -5

Combine like terms: 5 + -5 = 0
0 + -1r = 0 + -5
-1r = 0 + -5

Combine like terms: 0 + -5 = -5
-1r = -5

Divide each side by '-1'.
r = 5

Simplifying
r = 5
Solution
r = {3, 5}