(11r+6)(5r-2)=0

Solution for (11r+6)(5r-2)=0 equation:

Simplifying
(11r + 6)(5r + -2) = 0

Reorder the terms:
(6 + 11r)(5r + -2) = 0

Reorder the terms:
(6 + 11r)(-2 + 5r) = 0

Multiply (6 + 11r) * (-2 + 5r)
(6(-2 + 5r) + 11r * (-2 + 5r)) = 0
((-2 * 6 + 5r * 6) + 11r * (-2 + 5r)) = 0
((-12 + 30r) + 11r * (-2 + 5r)) = 0
(-12 + 30r + (-2 * 11r + 5r * 11r)) = 0
(-12 + 30r + (-22r + 55r2)) = 0

Combine like terms: 30r + -22r = 8r
(-12 + 8r + 55r2) = 0

Solving
-12 + 8r + 55r2 = 0

Solving for variable 'r'.

Factor a trinomial.
(-6 + -11r)(2 + -5r) = 0

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 '(2 + -5r)' equal to zero and attempt to solve:

Simplifying
2 + -5r = 0

Solving
2 + -5r = 0

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

Add '-2' to each side of the equation.
2 + -2 + -5r = 0 + -2

Combine like terms: 2 + -2 = 0
0 + -5r = 0 + -2
-5r = 0 + -2

Combine like terms: 0 + -2 = -2
-5r = -2

Divide each side by '-5'.
r = 0.4

Simplifying
r = 0.4
Solution
r = {-0.5454545455, 0.4}