(11r+9)(2r-6)=0

Solution for (11r+9)(2r-6)=0 equation:

Simplifying
(11r + 9)(2r + -6) = 0

Reorder the terms:
(9 + 11r)(2r + -6) = 0

Reorder the terms:
(9 + 11r)(-6 + 2r) = 0

Multiply (9 + 11r) * (-6 + 2r)
(9(-6 + 2r) + 11r * (-6 + 2r)) = 0
((-6 * 9 + 2r * 9) + 11r * (-6 + 2r)) = 0
((-54 + 18r) + 11r * (-6 + 2r)) = 0
(-54 + 18r + (-6 * 11r + 2r * 11r)) = 0
(-54 + 18r + (-66r + 22r2)) = 0

Combine like terms: 18r + -66r = -48r
(-54 + -48r + 22r2) = 0

Solving
-54 + -48r + 22r2 = 0

Solving for variable 'r'.

Factor out the Greatest Common Factor (GCF), '2'.
2(-27 + -24r + 11r2) = 0

Factor a trinomial.
2((-9 + -11r)(3 + -1r)) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(-9 + -11r)' equal to zero and attempt to solve:

Simplifying
-9 + -11r = 0

Solving
-9 + -11r = 0

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

Add '9' to each side of the equation.
-9 + 9 + -11r = 0 + 9

Combine like terms: -9 + 9 = 0
0 + -11r = 0 + 9
-11r = 0 + 9

Combine like terms: 0 + 9 = 9
-11r = 9

Divide each side by '-11'.
r = -0.8181818182

Simplifying
r = -0.8181818182
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 = {-0.8181818182, 3}