r^2=6r+27

Solution for r^2=6r+27 equation:

Simplifying
r2 = 6r + 27

Reorder the terms:
r2 = 27 + 6r

Solving
r2 = 27 + 6r

Solving for variable 'r'.

Reorder the terms:
-27 + -6r + r2 = 27 + 6r + -27 + -6r

Reorder the terms:
-27 + -6r + r2 = 27 + -27 + 6r + -6r

Combine like terms: 27 + -27 = 0
-27 + -6r + r2 = 0 + 6r + -6r
-27 + -6r + r2 = 6r + -6r

Combine like terms: 6r + -6r = 0
-27 + -6r + r2 = 0

Factor a trinomial.
(-3 + -1r)(9 + -1r) = 0

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

Simplifying
-3 + -1r = 0

Solving
-3 + -1r = 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 + -1r = 0 + 3

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

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

Divide each side by '-1'.
r = -3

Simplifying
r = -3
Subproblem 2
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
Solution
r = {-3, 9}