4r^2+32r+55=0

Solution for 4r^2+32r+55=0 equation:

Simplifying
4r2 + 32r + 55 = 0

Reorder the terms:
55 + 32r + 4r2 = 0

Solving
55 + 32r + 4r2 = 0

Solving for variable 'r'.

Factor a trinomial.
(11 + 2r)(5 + 2r) = 0

Subproblem 1
Set the factor '(11 + 2r)' equal to zero and attempt to solve:

Simplifying
11 + 2r = 0

Solving
11 + 2r = 0

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

Add '-11' to each side of the equation.
11 + -11 + 2r = 0 + -11

Combine like terms: 11 + -11 = 0
0 + 2r = 0 + -11
2r = 0 + -11

Combine like terms: 0 + -11 = -11
2r = -11

Divide each side by '2'.
r = -5.5

Simplifying
r = -5.5
Subproblem 2
Set the factor '(5 + 2r)' equal to zero and attempt to solve:

Simplifying
5 + 2r = 0

Solving
5 + 2r = 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 + 2r = 0 + -5

Combine like terms: 5 + -5 = 0
0 + 2r = 0 + -5
2r = 0 + -5

Combine like terms: 0 + -5 = -5
2r = -5

Divide each side by '2'.
r = -2.5

Simplifying
r = -2.5
Solution
r = {-5.5, -2.5}