2r^2+13r+21=0

Solution for 2r^2+13r+21=0 equation:

Simplifying
2r2 + 13r + 21 = 0

Reorder the terms:
21 + 13r + 2r2 = 0

Solving
21 + 13r + 2r2 = 0

Solving for variable 'r'.

Factor a trinomial.
(7 + 2r)(3 + r) = 0

Subproblem 1
Set the factor '(7 + 2r)' equal to zero and attempt to solve:

Simplifying
7 + 2r = 0

Solving
7 + 2r = 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 + 2r = 0 + -7

Combine like terms: 7 + -7 = 0
0 + 2r = 0 + -7
2r = 0 + -7

Combine like terms: 0 + -7 = -7
2r = -7

Divide each side by '2'.
r = -3.5

Simplifying
r = -3.5
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 = {-3.5, -3}