(r+3)(r-4)=0

Solution for (r+3)(r-4)=0 equation:

Simplifying
(r + 3)(r + -4) = 0

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

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

Multiply (3 + r) * (-4 + r)
(3(-4 + r) + r(-4 + r)) = 0
((-4 * 3 + r * 3) + r(-4 + r)) = 0
((-12 + 3r) + r(-4 + r)) = 0
(-12 + 3r + (-4 * r + r * r)) = 0
(-12 + 3r + (-4r + r2)) = 0

Combine like terms: 3r + -4r = -1r
(-12 + -1r + r2) = 0

Solving
-12 + -1r + r2 = 0

Solving for variable 'r'.

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

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}