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

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

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

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

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

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

Combine like terms: -4r + 2r = -2r
2(-8 + -2r + r2) = 0
(-8 * 2 + -2r * 2 + r2 * 2) = 0
(-16 + -4r + 2r2) = 0

Solving
-16 + -4r + 2r2 = 0

Solving for variable 'r'.

Factor out the Greatest Common Factor (GCF), '2'.
2(-8 + -2r + r2) = 0

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

Ignore the factor 2.
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 '(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
Solution
r = {-2, 4}