(5r-3)(6r-5)=

Solution for (5r-3)(6r-5)= equation:

Simplifying
(5r + -3)(6r + -5) = 0

Reorder the terms:
(-3 + 5r)(6r + -5) = 0

Reorder the terms:
(-3 + 5r)(-5 + 6r) = 0

Multiply (-3 + 5r) * (-5 + 6r)
(-3(-5 + 6r) + 5r * (-5 + 6r)) = 0
((-5 * -3 + 6r * -3) + 5r * (-5 + 6r)) = 0
((15 + -18r) + 5r * (-5 + 6r)) = 0
(15 + -18r + (-5 * 5r + 6r * 5r)) = 0
(15 + -18r + (-25r + 30r2)) = 0

Combine like terms: -18r + -25r = -43r
(15 + -43r + 30r2) = 0

Solving
15 + -43r + 30r2 = 0

Solving for variable 'r'.

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

Subproblem 1
Set the factor '(3 + -5r)' equal to zero and attempt to solve:

Simplifying
3 + -5r = 0

Solving
3 + -5r = 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 + -5r = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -5r = 0 + -3
-5r = 0 + -3

Combine like terms: 0 + -3 = -3
-5r = -3

Divide each side by '-5'.
r = 0.6

Simplifying
r = 0.6
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 = {0.6, 0.8333333333}