2r^2-3r=9

Solution for 2r^2-3r=9 equation:

Simplifying
2r2 + -3r = 9

Reorder the terms:
-3r + 2r2 = 9

Solving
-3r + 2r2 = 9

Solving for variable 'r'.

Reorder the terms:
-9 + -3r + 2r2 = 9 + -9

Combine like terms: 9 + -9 = 0
-9 + -3r + 2r2 = 0

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

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}