54+9r-3r^2=

Solution for 54+9r-3r^2= equation:

Simplifying
54 + 9r + -3r2 = 0

Solving
54 + 9r + -3r2 = 0

Solving for variable 'r'.

Factor out the Greatest Common Factor (GCF), '3'.
3(18 + 3r + -1r2) = 0

Factor a trinomial.
3((6 + -1r)(3 + r)) = 0

Ignore the factor 3.
Subproblem 1
Set the factor '(6 + -1r)' equal to zero and attempt to solve:

Simplifying
6 + -1r = 0

Solving
6 + -1r = 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 + -1r = 0 + -6

Combine like terms: 6 + -6 = 0
0 + -1r = 0 + -6
-1r = 0 + -6

Combine like terms: 0 + -6 = -6
-1r = -6

Divide each side by '-1'.
r = 6

Simplifying
r = 6
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 = {6, -3}