4r^2+21r+27=0

Solution for 4r^2+21r+27=0 equation:

Simplifying
4r2 + 21r + 27 = 0

Reorder the terms:
27 + 21r + 4r2 = 0

Solving
27 + 21r + 4r2 = 0

Solving for variable 'r'.

Factor a trinomial.
(3 + r)(9 + 4r) = 0

Subproblem 1
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
Subproblem 2
Set the factor '(9 + 4r)' equal to zero and attempt to solve:

Simplifying
9 + 4r = 0

Solving
9 + 4r = 0

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

Add '-9' to each side of the equation.
9 + -9 + 4r = 0 + -9

Combine like terms: 9 + -9 = 0
0 + 4r = 0 + -9
4r = 0 + -9

Combine like terms: 0 + -9 = -9
4r = -9

Divide each side by '4'.
r = -2.25

Simplifying
r = -2.25
Solution
r = {-3, -2.25}