(11r+6)(5r-15)=0

Solution for (11r+6)(5r-15)=0 equation:

Simplifying
(11r + 6)(5r + -15) = 0

Reorder the terms:
(6 + 11r)(5r + -15) = 0

Reorder the terms:
(6 + 11r)(-15 + 5r) = 0

Multiply (6 + 11r) * (-15 + 5r)
(6(-15 + 5r) + 11r * (-15 + 5r)) = 0
((-15 * 6 + 5r * 6) + 11r * (-15 + 5r)) = 0
((-90 + 30r) + 11r * (-15 + 5r)) = 0
(-90 + 30r + (-15 * 11r + 5r * 11r)) = 0
(-90 + 30r + (-165r + 55r2)) = 0

Combine like terms: 30r + -165r = -135r
(-90 + -135r + 55r2) = 0

Solving
-90 + -135r + 55r2 = 0

Solving for variable 'r'.

Factor out the Greatest Common Factor (GCF), '5'.
5(-18 + -27r + 11r2) = 0

Factor a trinomial.
5((-6 + -11r)(3 + -1r)) = 0

Ignore the factor 5.
Subproblem 1
Set the factor '(-6 + -11r)' equal to zero and attempt to solve:

Simplifying
-6 + -11r = 0

Solving
-6 + -11r = 0

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

Add '6' to each side of the equation.
-6 + 6 + -11r = 0 + 6

Combine like terms: -6 + 6 = 0
0 + -11r = 0 + 6
-11r = 0 + 6

Combine like terms: 0 + 6 = 6
-11r = 6

Divide each side by '-11'.
r = -0.5454545455

Simplifying
r = -0.5454545455
Subproblem 2
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
Solution
r = {-0.5454545455, 3}