3r^2+14r+15=0

Solution for 3r^2+14r+15=0 equation:

Simplifying
3r2 + 14r + 15 = 0

Reorder the terms:
15 + 14r + 3r2 = 0

Solving
15 + 14r + 3r2 = 0

Solving for variable 'r'.

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

Subproblem 1
Set the factor '(3 + r)' equal to zero and attempt to solve:

Simplifying
3 + r = 0

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

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

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

Simplifying
r = -3
Subproblem 2
Set the factor '(5 + 3r)' equal to zero and attempt to solve:

Simplifying
5 + 3r = 0

Solving
5 + 3r = 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 + 3r = 0 + -5

Combine like terms: 5 + -5 = 0
0 + 3r = 0 + -5
3r = 0 + -5

Combine like terms: 0 + -5 = -5
3r = -5

Divide each side by '3'.
r = -1.666666667

Simplifying
r = -1.666666667
Solution
r = {-3, -1.666666667}