2r^2+9r+15=-4r

Solution for 2r^2+9r+15=-4r equation:

Simplifying
2r2 + 9r + 15 = -4r

Reorder the terms:
15 + 9r + 2r2 = -4r

Solving
15 + 9r + 2r2 = -4r

Solving for variable 'r'.

Reorder the terms:
15 + 9r + 4r + 2r2 = -4r + 4r

Combine like terms: 9r + 4r = 13r
15 + 13r + 2r2 = -4r + 4r

Combine like terms: -4r + 4r = 0
15 + 13r + 2r2 = 0

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

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

Simplifying
5 + r = 0

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

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

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

Simplifying
r = -5
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 = {-5, -1.5}