(r+3)(r-7)=0

Solution for (r+3)(r-7)=0 equation:

Simplifying
(r + 3)(r + -7) = 0

Reorder the terms:
(3 + r)(r + -7) = 0

Reorder the terms:
(3 + r)(-7 + r) = 0

Multiply (3 + r) * (-7 + r)
(3(-7 + r) + r(-7 + r)) = 0
((-7 * 3 + r * 3) + r(-7 + r)) = 0
((-21 + 3r) + r(-7 + r)) = 0
(-21 + 3r + (-7 * r + r * r)) = 0
(-21 + 3r + (-7r + r2)) = 0

Combine like terms: 3r + -7r = -4r
(-21 + -4r + r2) = 0

Solving
-21 + -4r + r2 = 0

Solving for variable 'r'.

Factor a trinomial.
(-3 + -1r)(7 + -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 '(7 + -1r)' equal to zero and attempt to solve:

Simplifying
7 + -1r = 0

Solving
7 + -1r = 0

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

Add '-7' to each side of the equation.
7 + -7 + -1r = 0 + -7

Combine like terms: 7 + -7 = 0
0 + -1r = 0 + -7
-1r = 0 + -7

Combine like terms: 0 + -7 = -7
-1r = -7

Divide each side by '-1'.
r = 7

Simplifying
r = 7
Solution
r = {-3, 7}