2r^2-3r=27

Solution for 2r^2-3r=27 equation:

Simplifying
2r2 + -3r = 27

Reorder the terms:
-3r + 2r2 = 27

Solving
-3r + 2r2 = 27

Solving for variable 'r'.

Reorder the terms:
-27 + -3r + 2r2 = 27 + -27

Combine like terms: 27 + -27 = 0
-27 + -3r + 2r2 = 0

Factor a trinomial.
(-3 + -1r)(9 + -2r) = 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 + -2r)' equal to zero and attempt to solve:

Simplifying
9 + -2r = 0

Solving
9 + -2r = 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 + -2r = 0 + -9

Combine like terms: 9 + -9 = 0
0 + -2r = 0 + -9
-2r = 0 + -9

Combine like terms: 0 + -9 = -9
-2r = -9

Divide each side by '-2'.
r = 4.5

Simplifying
r = 4.5
Solution
r = {-3, 4.5}