2r^2+21r+54=0

Solution for 2r^2+21r+54=0 equation:

Simplifying
2r2 + 21r + 54 = 0

Reorder the terms:
54 + 21r + 2r2 = 0

Solving
54 + 21r + 2r2 = 0

Solving for variable 'r'.

Factor a trinomial.
(6 + r)(9 + 2r) = 0

Subproblem 1
Set the factor '(6 + r)' equal to zero and attempt to solve:

Simplifying
6 + r = 0

Solving
6 + r = 0

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

Add '-6' to each side of the equation.
6 + -6 + r = 0 + -6

Combine like terms: 6 + -6 = 0
0 + r = 0 + -6
r = 0 + -6

Combine like terms: 0 + -6 = -6
r = -6

Simplifying
r = -6
Subproblem 2
Set the factor '(9 + 2r)' equal to zero and attempt to solve:

Simplifying
9 + 2r = 0

Solving
9 + 2r = 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 + 2r = 0 + -9

Combine like terms: 9 + -9 = 0
0 + 2r = 0 + -9
2r = 0 + -9

Combine like terms: 0 + -9 = -9
2r = -9

Divide each side by '2'.
r = -4.5

Simplifying
r = -4.5
Solution
r = {-6, -4.5}