(5r+11)(r+10)=0

Solution for (5r+11)(r+10)=0 equation:

Simplifying
(5r + 11)(r + 10) = 0

Reorder the terms:
(11 + 5r)(r + 10) = 0

Reorder the terms:
(11 + 5r)(10 + r) = 0

Multiply (11 + 5r) * (10 + r)
(11(10 + r) + 5r * (10 + r)) = 0
((10 * 11 + r * 11) + 5r * (10 + r)) = 0
((110 + 11r) + 5r * (10 + r)) = 0
(110 + 11r + (10 * 5r + r * 5r)) = 0
(110 + 11r + (50r + 5r2)) = 0

Combine like terms: 11r + 50r = 61r
(110 + 61r + 5r2) = 0

Solving
110 + 61r + 5r2 = 0

Solving for variable 'r'.

Factor a trinomial.
(10 + r)(11 + 5r) = 0

Subproblem 1
Set the factor '(10 + r)' equal to zero and attempt to solve:

Simplifying
10 + r = 0

Solving
10 + r = 0

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

Add '-10' to each side of the equation.
10 + -10 + r = 0 + -10

Combine like terms: 10 + -10 = 0
0 + r = 0 + -10
r = 0 + -10

Combine like terms: 0 + -10 = -10
r = -10

Simplifying
r = -10
Subproblem 2
Set the factor '(11 + 5r)' equal to zero and attempt to solve:

Simplifying
11 + 5r = 0

Solving
11 + 5r = 0

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

Add '-11' to each side of the equation.
11 + -11 + 5r = 0 + -11

Combine like terms: 11 + -11 = 0
0 + 5r = 0 + -11
5r = 0 + -11

Combine like terms: 0 + -11 = -11
5r = -11

Divide each side by '5'.
r = -2.2

Simplifying
r = -2.2
Solution
r = {-10, -2.2}