(-4r-1)(-9r-1)=0

Solution for (-4r-1)(-9r-1)=0 equation:

Simplifying
(-4r + -1)(-9r + -1) = 0

Reorder the terms:
(-1 + -4r)(-9r + -1) = 0

Reorder the terms:
(-1 + -4r)(-1 + -9r) = 0

Multiply (-1 + -4r) * (-1 + -9r)
(-1(-1 + -9r) + -4r * (-1 + -9r)) = 0
((-1 * -1 + -9r * -1) + -4r * (-1 + -9r)) = 0
((1 + 9r) + -4r * (-1 + -9r)) = 0
(1 + 9r + (-1 * -4r + -9r * -4r)) = 0
(1 + 9r + (4r + 36r2)) = 0

Combine like terms: 9r + 4r = 13r
(1 + 13r + 36r2) = 0

Solving
1 + 13r + 36r2 = 0

Solving for variable 'r'.

Factor a trinomial.
(1 + 4r)(1 + 9r) = 0

Subproblem 1
Set the factor '(1 + 4r)' equal to zero and attempt to solve:

Simplifying
1 + 4r = 0

Solving
1 + 4r = 0

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

Add '-1' to each side of the equation.
1 + -1 + 4r = 0 + -1

Combine like terms: 1 + -1 = 0
0 + 4r = 0 + -1
4r = 0 + -1

Combine like terms: 0 + -1 = -1
4r = -1

Divide each side by '4'.
r = -0.25

Simplifying
r = -0.25
Subproblem 2
Set the factor '(1 + 9r)' equal to zero and attempt to solve:

Simplifying
1 + 9r = 0

Solving
1 + 9r = 0

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

Add '-1' to each side of the equation.
1 + -1 + 9r = 0 + -1

Combine like terms: 1 + -1 = 0
0 + 9r = 0 + -1
9r = 0 + -1

Combine like terms: 0 + -1 = -1
9r = -1

Divide each side by '9'.
r = -0.1111111111

Simplifying
r = -0.1111111111
Solution
r = {-0.25, -0.1111111111}