6r+r^2=27

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

Simplifying
6r + r2 = 27

Solving
6r + r2 = 27

Solving for variable 'r'.

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

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

Factor a trinomial.
(-9 + -1r)(3 + -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 '(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
Solution
r = {-9, 3}