2r^2+11r+14=0

Solution for 2r^2+11r+14=0 equation:

Simplifying
2r2 + 11r + 14 = 0

Reorder the terms:
14 + 11r + 2r2 = 0

Solving
14 + 11r + 2r2 = 0

Solving for variable 'r'.

Factor a trinomial.
(7 + 2r)(2 + 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 '(2 + r)' equal to zero and attempt to solve:

Simplifying
2 + r = 0

Solving
2 + r = 0

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

Add '-2' to each side of the equation.
2 + -2 + r = 0 + -2

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

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

Simplifying
r = -2
Solution
r = {-3.5, -2}