7r^2+49r+84=0

Solution for 7r^2+49r+84=0 equation:

Simplifying
7r2 + 49r + 84 = 0

Reorder the terms:
84 + 49r + 7r2 = 0

Solving
84 + 49r + 7r2 = 0

Solving for variable 'r'.

Factor out the Greatest Common Factor (GCF), '7'.
7(12 + 7r + r2) = 0

Factor a trinomial.
7((4 + r)(3 + r)) = 0

Ignore the factor 7.
Subproblem 1
Set the factor '(4 + r)' equal to zero and attempt to solve:

Simplifying
4 + r = 0

Solving
4 + r = 0

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

Add '-4' to each side of the equation.
4 + -4 + r = 0 + -4

Combine like terms: 4 + -4 = 0
0 + r = 0 + -4
r = 0 + -4

Combine like terms: 0 + -4 = -4
r = -4

Simplifying
r = -4
Subproblem 2
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
Solution
r = {-4, -3}