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

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

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

Reorder the terms:
r(5 + 2r) + 6(2r + 5) = 0
(5 * r + 2r * r) + 6(2r + 5) = 0
(5r + 2r2) + 6(2r + 5) = 0

Reorder the terms:
5r + 2r2 + 6(5 + 2r) = 0
5r + 2r2 + (5 * 6 + 2r * 6) = 0
5r + 2r2 + (30 + 12r) = 0

Reorder the terms:
30 + 5r + 12r + 2r2 = 0

Combine like terms: 5r + 12r = 17r
30 + 17r + 2r2 = 0

Solving
30 + 17r + 2r2 = 0

Solving for variable 'r'.

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

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

Simplifying
6 + r = 0

Solving
6 + r = 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 + r = 0 + -6

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

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

Simplifying
r = -6
Subproblem 2
Set the factor '(5 + 2r)' equal to zero and attempt to solve:

Simplifying
5 + 2r = 0

Solving
5 + 2r = 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 + 2r = 0 + -5

Combine like terms: 5 + -5 = 0
0 + 2r = 0 + -5
2r = 0 + -5

Combine like terms: 0 + -5 = -5
2r = -5

Divide each side by '2'.
r = -2.5

Simplifying
r = -2.5
Solution
r = {-6, -2.5}