(5r-1)(6r-3)=

Solution for (5r-1)(6r-3)= equation:

Simplifying
(5r + -1)(6r + -3) = 0

Reorder the terms:
(-1 + 5r)(6r + -3) = 0

Reorder the terms:
(-1 + 5r)(-3 + 6r) = 0

Multiply (-1 + 5r) * (-3 + 6r)
(-1(-3 + 6r) + 5r * (-3 + 6r)) = 0
((-3 * -1 + 6r * -1) + 5r * (-3 + 6r)) = 0
((3 + -6r) + 5r * (-3 + 6r)) = 0
(3 + -6r + (-3 * 5r + 6r * 5r)) = 0
(3 + -6r + (-15r + 30r2)) = 0

Combine like terms: -6r + -15r = -21r
(3 + -21r + 30r2) = 0

Solving
3 + -21r + 30r2 = 0

Solving for variable 'r'.

Factor out the Greatest Common Factor (GCF), '3'.
3(1 + -7r + 10r2) = 0

Factor a trinomial.
3((1 + -5r)(1 + -2r)) = 0

Ignore the factor 3.
Subproblem 1
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
Subproblem 2
Set the factor '(1 + -2r)' equal to zero and attempt to solve:

Simplifying
1 + -2r = 0

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

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

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

Divide each side by '-2'.
r = 0.5

Simplifying
r = 0.5
Solution
r = {0.2, 0.5}