(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 = 9r
(-3 + 9r + 30r2) = 0

Solving
-3 + 9r + 30r2 = 0

Solving for variable 'r'.

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

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

Ignore the factor 3.
Subproblem 1
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
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 = {-0.5, 0.2}