2r^2+15r+24=6

Solution for 2r^2+15r+24=6 equation:

Simplifying
2r2 + 15r + 24 = 6

Reorder the terms:
24 + 15r + 2r2 = 6

Solving
24 + 15r + 2r2 = 6

Solving for variable 'r'.

Reorder the terms:
24 + -6 + 15r + 2r2 = 6 + -6

Combine like terms: 24 + -6 = 18
18 + 15r + 2r2 = 6 + -6

Combine like terms: 6 + -6 = 0
18 + 15r + 2r2 = 0

Factor a trinomial.
(6 + r)(3 + 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 '(3 + 2r)' equal to zero and attempt to solve:

Simplifying
3 + 2r = 0

Solving
3 + 2r = 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 + 2r = 0 + -3

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

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

Divide each side by '2'.
r = -1.5

Simplifying
r = -1.5
Solution
r = {-6, -1.5}