(r-2)(r+4)=0

Solution for (r-2)(r+4)=0 equation:

Simplifying
(r + -2)(r + 4) = 0

Reorder the terms:
(-2 + r)(r + 4) = 0

Reorder the terms:
(-2 + r)(4 + r) = 0

Multiply (-2 + r) * (4 + r)
(-2(4 + r) + r(4 + r)) = 0
((4 * -2 + r * -2) + r(4 + r)) = 0
((-8 + -2r) + r(4 + r)) = 0
(-8 + -2r + (4 * r + r * r)) = 0
(-8 + -2r + (4r + r2)) = 0

Combine like terms: -2r + 4r = 2r
(-8 + 2r + r2) = 0

Solving
-8 + 2r + r2 = 0

Solving for variable 'r'.

Factor a trinomial.
(-4 + -1r)(2 + -1r) = 0

Subproblem 1
Set the factor '(-4 + -1r)' equal to zero and attempt to solve:

Simplifying
-4 + -1r = 0

Solving
-4 + -1r = 0

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

Add '4' to each side of the equation.
-4 + 4 + -1r = 0 + 4

Combine like terms: -4 + 4 = 0
0 + -1r = 0 + 4
-1r = 0 + 4

Combine like terms: 0 + 4 = 4
-1r = 4

Divide each side by '-1'.
r = -4

Simplifying
r = -4
Subproblem 2
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
Solution
r = {-4, 2}