6r^2-9r=27

Solution for 6r^2-9r=27 equation:

Simplifying
6r2 + -9r = 27

Reorder the terms:
-9r + 6r2 = 27

Solving
-9r + 6r2 = 27

Solving for variable 'r'.

Reorder the terms:
-27 + -9r + 6r2 = 27 + -27

Combine like terms: 27 + -27 = 0
-27 + -9r + 6r2 = 0

Factor out the Greatest Common Factor (GCF), '3'.
3(-9 + -3r + 2r2) = 0

Factor a trinomial.
3((-3 + -2r)(3 + -1r)) = 0

Ignore the factor 3.
Subproblem 1
Set the factor '(-3 + -2r)' equal to zero and attempt to solve:

Simplifying
-3 + -2r = 0

Solving
-3 + -2r = 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 + -2r = 0 + 3

Combine like terms: -3 + 3 = 0
0 + -2r = 0 + 3
-2r = 0 + 3

Combine like terms: 0 + 3 = 3
-2r = 3

Divide each side by '-2'.
r = -1.5

Simplifying
r = -1.5
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 = {-1.5, 3}