5r^2-18r=-9

Solution for 5r^2-18r=-9 equation:

Simplifying
5r2 + -18r = -9

Reorder the terms:
-18r + 5r2 = -9

Solving
-18r + 5r2 = -9

Solving for variable 'r'.

Reorder the terms:
9 + -18r + 5r2 = -9 + 9

Combine like terms: -9 + 9 = 0
9 + -18r + 5r2 = 0

Factor a trinomial.
(3 + -5r)(3 + -1r) = 0

Subproblem 1
Set the factor '(3 + -5r)' equal to zero and attempt to solve:

Simplifying
3 + -5r = 0

Solving
3 + -5r = 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 + -5r = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -5r = 0 + -3
-5r = 0 + -3

Combine like terms: 0 + -3 = -3
-5r = -3

Divide each side by '-5'.
r = 0.6

Simplifying
r = 0.6
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 = {0.6, 3}