r^2=54-3r

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

Simplifying
r2 = 54 + -3r

Solving
r2 = 54 + -3r

Solving for variable 'r'.

Reorder the terms:
-54 + 3r + r2 = 54 + -3r + -54 + 3r

Reorder the terms:
-54 + 3r + r2 = 54 + -54 + -3r + 3r

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

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

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

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

Simplifying
-9 + -1r = 0

Solving
-9 + -1r = 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 + -1r = 0 + 9

Combine like terms: -9 + 9 = 0
0 + -1r = 0 + 9
-1r = 0 + 9

Combine like terms: 0 + 9 = 9
-1r = 9

Divide each side by '-1'.
r = -9

Simplifying
r = -9
Subproblem 2
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
Solution
r = {-9, 6}