(5r-1)(6r+5)=0

Solution for (5r-1)(6r+5)=0 equation:

Simplifying
(5r + -1)(6r + 5) = 0

Reorder the terms:
(-1 + 5r)(6r + 5) = 0

Reorder the terms:
(-1 + 5r)(5 + 6r) = 0

Multiply (-1 + 5r) * (5 + 6r)
(-1(5 + 6r) + 5r * (5 + 6r)) = 0
((5 * -1 + 6r * -1) + 5r * (5 + 6r)) = 0
((-5 + -6r) + 5r * (5 + 6r)) = 0
(-5 + -6r + (5 * 5r + 6r * 5r)) = 0
(-5 + -6r + (25r + 30r2)) = 0

Combine like terms: -6r + 25r = 19r
(-5 + 19r + 30r2) = 0

Solving
-5 + 19r + 30r2 = 0

Solving for variable 'r'.

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

Subproblem 1
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
Subproblem 2
Set the factor '(1 + -5r)' equal to zero and attempt to solve:

Simplifying
1 + -5r = 0

Solving
1 + -5r = 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 + -5r = 0 + -1

Combine like terms: 1 + -1 = 0
0 + -5r = 0 + -1
-5r = 0 + -1

Combine like terms: 0 + -1 = -1
-5r = -1

Divide each side by '-5'.
r = 0.2

Simplifying
r = 0.2
Solution
r = {-0.8333333333, 0.2}