7r^2+91r+280=0

Solution for 7r^2+91r+280=0 equation:

Simplifying
7r2 + 91r + 280 = 0

Reorder the terms:
280 + 91r + 7r2 = 0

Solving
280 + 91r + 7r2 = 0

Solving for variable 'r'.

Factor out the Greatest Common Factor (GCF), '7'.
7(40 + 13r + r2) = 0

Factor a trinomial.
7((8 + r)(5 + r)) = 0

Ignore the factor 7.
Subproblem 1
Set the factor '(8 + r)' equal to zero and attempt to solve:

Simplifying
8 + r = 0

Solving
8 + r = 0

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

Add '-8' to each side of the equation.
8 + -8 + r = 0 + -8

Combine like terms: 8 + -8 = 0
0 + r = 0 + -8
r = 0 + -8

Combine like terms: 0 + -8 = -8
r = -8

Simplifying
r = -8
Subproblem 2
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
Solution
r = {-8, -5}