27=6r+r^2

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

Simplifying
27 = 6r + r2

Solving
27 = 6r + r2

Solving for variable 'r'.

Reorder the terms:
27 + -6r + -1r2 = 6r + -6r + r2 + -1r2

Combine like terms: 6r + -6r = 0
27 + -6r + -1r2 = 0 + r2 + -1r2
27 + -6r + -1r2 = r2 + -1r2

Combine like terms: r2 + -1r2 = 0
27 + -6r + -1r2 = 0

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