(r+2)(r-6)=0

Solution for (r+2)(r-6)=0 equation:

Simplifying
(r + 2)(r + -6) = 0

Reorder the terms:
(2 + r)(r + -6) = 0

Reorder the terms:
(2 + r)(-6 + r) = 0

Multiply (2 + r) * (-6 + r)
(2(-6 + r) + r(-6 + r)) = 0
((-6 * 2 + r * 2) + r(-6 + r)) = 0
((-12 + 2r) + r(-6 + r)) = 0
(-12 + 2r + (-6 * r + r * r)) = 0
(-12 + 2r + (-6r + r2)) = 0

Combine like terms: 2r + -6r = -4r
(-12 + -4r + r2) = 0

Solving
-12 + -4r + r2 = 0

Solving for variable 'r'.

Factor a trinomial.
(-2 + -1r)(6 + -1r) = 0

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

Simplifying
-2 + -1r = 0

Solving
-2 + -1r = 0

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

Add '2' to each side of the equation.
-2 + 2 + -1r = 0 + 2

Combine like terms: -2 + 2 = 0
0 + -1r = 0 + 2
-1r = 0 + 2

Combine like terms: 0 + 2 = 2
-1r = 2

Divide each side by '-1'.
r = -2

Simplifying
r = -2
Subproblem 2
Set the factor '(6 + -1r)' equal to zero and attempt to solve:

Simplifying
6 + -1r = 0

Solving
6 + -1r = 0

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

Add '-6' to each side of the equation.
6 + -6 + -1r = 0 + -6

Combine like terms: 6 + -6 = 0
0 + -1r = 0 + -6
-1r = 0 + -6

Combine like terms: 0 + -6 = -6
-1r = -6

Divide each side by '-1'.
r = 6

Simplifying
r = 6
Solution
r = {-2, 6}