(3r+5)(2r-6)=

Solution for (3r+5)(2r-6)= equation:

Simplifying
(3r + 5)(2r + -6) = 0

Reorder the terms:
(5 + 3r)(2r + -6) = 0

Reorder the terms:
(5 + 3r)(-6 + 2r) = 0

Multiply (5 + 3r) * (-6 + 2r)
(5(-6 + 2r) + 3r * (-6 + 2r)) = 0
((-6 * 5 + 2r * 5) + 3r * (-6 + 2r)) = 0
((-30 + 10r) + 3r * (-6 + 2r)) = 0
(-30 + 10r + (-6 * 3r + 2r * 3r)) = 0
(-30 + 10r + (-18r + 6r2)) = 0

Combine like terms: 10r + -18r = -8r
(-30 + -8r + 6r2) = 0

Solving
-30 + -8r + 6r2 = 0

Solving for variable 'r'.

Factor out the Greatest Common Factor (GCF), '2'.
2(-15 + -4r + 3r2) = 0

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

Ignore the factor 2.
Subproblem 1
Set the factor '(-5 + -3r)' equal to zero and attempt to solve:

Simplifying
-5 + -3r = 0

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

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

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

Divide each side by '-3'.
r = -1.666666667

Simplifying
r = -1.666666667
Subproblem 2
Set the factor '(3 + -1r)' equal to zero and attempt to solve:

Simplifying
3 + -1r = 0

Solving
3 + -1r = 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 + -1r = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -1r = 0 + -3
-1r = 0 + -3

Combine like terms: 0 + -3 = -3
-1r = -3

Divide each side by '-1'.
r = 3

Simplifying
r = 3
Solution
r = {-1.666666667, 3}