(r-4)(2r+6)=0

Solution for (r-4)(2r+6)=0 equation:

Simplifying
(r + -4)(2r + 6) = 0

Reorder the terms:
(-4 + r)(2r + 6) = 0

Reorder the terms:
(-4 + r)(6 + 2r) = 0

Multiply (-4 + r) * (6 + 2r)
(-4(6 + 2r) + r(6 + 2r)) = 0
((6 * -4 + 2r * -4) + r(6 + 2r)) = 0
((-24 + -8r) + r(6 + 2r)) = 0
(-24 + -8r + (6 * r + 2r * r)) = 0
(-24 + -8r + (6r + 2r2)) = 0

Combine like terms: -8r + 6r = -2r
(-24 + -2r + 2r2) = 0

Solving
-24 + -2r + 2r2 = 0

Solving for variable 'r'.

Factor out the Greatest Common Factor (GCF), '2'.
2(-12 + -1r + r2) = 0

Factor a trinomial.
2((-3 + -1r)(4 + -1r)) = 0

Ignore the factor 2.
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 '(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 = {-3, 4}