(r-6)(r+4)=

Solution for (r-6)(r+4)= equation:

Simplifying
(r + -6)(r + 4) = 0

Reorder the terms:
(-6 + r)(r + 4) = 0

Reorder the terms:
(-6 + r)(4 + r) = 0

Multiply (-6 + r) * (4 + r)
(-6(4 + r) + r(4 + r)) = 0
((4 * -6 + r * -6) + r(4 + r)) = 0
((-24 + -6r) + r(4 + r)) = 0
(-24 + -6r + (4 * r + r * r)) = 0
(-24 + -6r + (4r + r2)) = 0

Combine like terms: -6r + 4r = -2r
(-24 + -2r + r2) = 0

Solving
-24 + -2r + r2 = 0

Solving for variable 'r'.

Factor a trinomial.
(-4 + -1r)(6 + -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 '(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 = {-4, 6}