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

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

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

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

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

Multiply (2 + r) * (-5 + 6r)
(2(-5 + 6r) + r(-5 + 6r)) = 0
((-5 * 2 + 6r * 2) + r(-5 + 6r)) = 0
((-10 + 12r) + r(-5 + 6r)) = 0
(-10 + 12r + (-5 * r + 6r * r)) = 0
(-10 + 12r + (-5r + 6r2)) = 0

Combine like terms: 12r + -5r = 7r
(-10 + 7r + 6r2) = 0

Solving
-10 + 7r + 6r2 = 0

Solving for variable 'r'.

Factor a trinomial.
(-2 + -1r)(5 + -6r) = 0

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

Simplifying
-2 + -1r = 0

Solving
-2 + -1r = 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 + -1r = 0 + 2

Combine like terms: -2 + 2 = 0
0 + -1r = 0 + 2
-1r = 0 + 2

Combine like terms: 0 + 2 = 2
-1r = 2

Divide each side by '-1'.
r = -2

Simplifying
r = -2
Subproblem 2
Set the factor '(5 + -6r)' equal to zero and attempt to solve:

Simplifying
5 + -6r = 0

Solving
5 + -6r = 0

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

Add '-5' to each side of the equation.
5 + -5 + -6r = 0 + -5

Combine like terms: 5 + -5 = 0
0 + -6r = 0 + -5
-6r = 0 + -5

Combine like terms: 0 + -5 = -5
-6r = -5

Divide each side by '-6'.
r = 0.8333333333

Simplifying
r = 0.8333333333
Solution
r = {-2, 0.8333333333}