5r^2-18=27r

Solution for 5r^2-18=27r equation:

Simplifying
5r2 + -18 = 27r

Reorder the terms:
-18 + 5r2 = 27r

Solving
-18 + 5r2 = 27r

Solving for variable 'r'.

Reorder the terms:
-18 + -27r + 5r2 = 27r + -27r

Combine like terms: 27r + -27r = 0
-18 + -27r + 5r2 = 0

Factor a trinomial.
(-3 + -5r)(6 + -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 '(6 + -1r)' equal to zero and attempt to solve:

Simplifying
6 + -1r = 0

Solving
6 + -1r = 0

Move all terms containing r to the left, all other terms to the right.

Add '-6' to each side of the equation.
6 + -6 + -1r = 0 + -6

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

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

Divide each side by '-1'.
r = 6

Simplifying
r = 6
Solution
r = {-0.6, 6}