54-3r=r^2

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

Simplifying
54 + -3r = r2

Solving
54 + -3r = r2

Solving for variable 'r'.

Combine like terms: r2 + -1r2 = 0
54 + -3r + -1r2 = 0

Factor a trinomial.
(6 + -1r)(9 + r) = 0

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 '(9 + r)' equal to zero and attempt to solve:

Simplifying
9 + r = 0

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

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

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

Simplifying
r = -9
Solution
r = {6, -9}