5r^2+65r=-210

Solution for 5r^2+65r=-210 equation:

Simplifying
5r2 + 65r = -210

Reorder the terms:
65r + 5r2 = -210

Solving
65r + 5r2 = -210

Solving for variable 'r'.

Reorder the terms:
210 + 65r + 5r2 = -210 + 210

Combine like terms: -210 + 210 = 0
210 + 65r + 5r2 = 0

Factor out the Greatest Common Factor (GCF), '5'.
5(42 + 13r + r2) = 0

Factor a trinomial.
5((7 + r)(6 + r)) = 0

Ignore the factor 5.
Subproblem 1
Set the factor '(7 + r)' equal to zero and attempt to solve:

Simplifying
7 + r = 0

Solving
7 + r = 0

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

Add '-7' to each side of the equation.
7 + -7 + r = 0 + -7

Combine like terms: 7 + -7 = 0
0 + r = 0 + -7
r = 0 + -7

Combine like terms: 0 + -7 = -7
r = -7

Simplifying
r = -7
Subproblem 2
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
Solution
r = {-7, -6}