4r^2+16r+15=0

Solution for 4r^2+16r+15=0 equation:

Simplifying
4r2 + 16r + 15 = 0

Reorder the terms:
15 + 16r + 4r2 = 0

Solving
15 + 16r + 4r2 = 0

Solving for variable 'r'.

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

Subproblem 1
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
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 = {-2.5, -1.5}