(r+16)(r+49)=0

Solution for (r+16)(r+49)=0 equation:

Simplifying
(r + 16)(r + 49) = 0

Reorder the terms:
(16 + r)(r + 49) = 0

Reorder the terms:
(16 + r)(49 + r) = 0

Multiply (16 + r) * (49 + r)
(16(49 + r) + r(49 + r)) = 0
((49 * 16 + r * 16) + r(49 + r)) = 0
((784 + 16r) + r(49 + r)) = 0
(784 + 16r + (49 * r + r * r)) = 0
(784 + 16r + (49r + r2)) = 0

Combine like terms: 16r + 49r = 65r
(784 + 65r + r2) = 0

Solving
784 + 65r + r2 = 0

Solving for variable 'r'.

Factor a trinomial.
(49 + r)(16 + r) = 0

Subproblem 1
Set the factor '(49 + r)' equal to zero and attempt to solve:

Simplifying
49 + r = 0

Solving
49 + r = 0

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

Add '-49' to each side of the equation.
49 + -49 + r = 0 + -49

Combine like terms: 49 + -49 = 0
0 + r = 0 + -49
r = 0 + -49

Combine like terms: 0 + -49 = -49
r = -49

Simplifying
r = -49
Subproblem 2
Set the factor '(16 + r)' equal to zero and attempt to solve:

Simplifying
16 + r = 0

Solving
16 + r = 0

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

Add '-16' to each side of the equation.
16 + -16 + r = 0 + -16

Combine like terms: 16 + -16 = 0
0 + r = 0 + -16
r = 0 + -16

Combine like terms: 0 + -16 = -16
r = -16

Simplifying
r = -16
Solution
r = {-49, -16}