3r^2+25r+50=0

Solution for 3r^2+25r+50=0 equation:

Simplifying
3r2 + 25r + 50 = 0

Reorder the terms:
50 + 25r + 3r2 = 0

Solving
50 + 25r + 3r2 = 0

Solving for variable 'r'.

Factor a trinomial.
(5 + r)(10 + 3r) = 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 '(10 + 3r)' equal to zero and attempt to solve:

Simplifying
10 + 3r = 0

Solving
10 + 3r = 0

Move all terms containing r to the left, all other terms to the right.

Add '-10' to each side of the equation.
10 + -10 + 3r = 0 + -10

Combine like terms: 10 + -10 = 0
0 + 3r = 0 + -10
3r = 0 + -10

Combine like terms: 0 + -10 = -10
3r = -10

Divide each side by '3'.
r = -3.333333333

Simplifying
r = -3.333333333
Solution
r = {-5, -3.333333333}