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

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

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

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

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

Multiply (6 + 5r) * (2 + 3r)
(6(2 + 3r) + 5r * (2 + 3r)) = 0
((2 * 6 + 3r * 6) + 5r * (2 + 3r)) = 0
((12 + 18r) + 5r * (2 + 3r)) = 0
(12 + 18r + (2 * 5r + 3r * 5r)) = 0
(12 + 18r + (10r + 15r2)) = 0

Combine like terms: 18r + 10r = 28r
(12 + 28r + 15r2) = 0

Solving
12 + 28r + 15r2 = 0

Solving for variable 'r'.

Factor a trinomial.
(6 + 5r)(2 + 3r) = 0

Subproblem 1
Set the factor '(6 + 5r)' equal to zero and attempt to solve:

Simplifying
6 + 5r = 0

Solving
6 + 5r = 0

Move all terms containing r to the left, all other terms to the right.

Add '-6' to each side of the equation.
6 + -6 + 5r = 0 + -6

Combine like terms: 6 + -6 = 0
0 + 5r = 0 + -6
5r = 0 + -6

Combine like terms: 0 + -6 = -6
5r = -6

Divide each side by '5'.
r = -1.2

Simplifying
r = -1.2
Subproblem 2
Set the factor '(2 + 3r)' equal to zero and attempt to solve:

Simplifying
2 + 3r = 0

Solving
2 + 3r = 0

Move all terms containing r to the left, all other terms to the right.

Add '-2' to each side of the equation.
2 + -2 + 3r = 0 + -2

Combine like terms: 2 + -2 = 0
0 + 3r = 0 + -2
3r = 0 + -2

Combine like terms: 0 + -2 = -2
3r = -2

Divide each side by '3'.
r = -0.6666666667

Simplifying
r = -0.6666666667
Solution
r = {-1.2, -0.6666666667}