(r+5)(r-12)=0

Solution for (r+5)(r-12)=0 equation:

Simplifying
(r + 5)(r + -12) = 0

Reorder the terms:
(5 + r)(r + -12) = 0

Reorder the terms:
(5 + r)(-12 + r) = 0

Multiply (5 + r) * (-12 + r)
(5(-12 + r) + r(-12 + r)) = 0
((-12 * 5 + r * 5) + r(-12 + r)) = 0
((-60 + 5r) + r(-12 + r)) = 0
(-60 + 5r + (-12 * r + r * r)) = 0
(-60 + 5r + (-12r + r2)) = 0

Combine like terms: 5r + -12r = -7r
(-60 + -7r + r2) = 0

Solving
-60 + -7r + r2 = 0

Solving for variable 'r'.

Factor a trinomial.
(-5 + -1r)(12 + -1r) = 0

Subproblem 1
Set the factor '(-5 + -1r)' equal to zero and attempt to solve:

Simplifying
-5 + -1r = 0

Solving
-5 + -1r = 0

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

Add '5' to each side of the equation.
-5 + 5 + -1r = 0 + 5

Combine like terms: -5 + 5 = 0
0 + -1r = 0 + 5
-1r = 0 + 5

Combine like terms: 0 + 5 = 5
-1r = 5

Divide each side by '-1'.
r = -5

Simplifying
r = -5
Subproblem 2
Set the factor '(12 + -1r)' equal to zero and attempt to solve:

Simplifying
12 + -1r = 0

Solving
12 + -1r = 0

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

Add '-12' to each side of the equation.
12 + -12 + -1r = 0 + -12

Combine like terms: 12 + -12 = 0
0 + -1r = 0 + -12
-1r = 0 + -12

Combine like terms: 0 + -12 = -12
-1r = -12

Divide each side by '-1'.
r = 12

Simplifying
r = 12
Solution
r = {-5, 12}