27r^2+36r-15=0

Solution for 27r^2+36r-15=0 equation:

Simplifying
27r2 + 36r + -15 = 0

Reorder the terms:
-15 + 36r + 27r2 = 0

Solving
-15 + 36r + 27r2 = 0

Solving for variable 'r'.

Factor out the Greatest Common Factor (GCF), '3'.
3(-5 + 12r + 9r2) = 0

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

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

Simplifying
-5 + -3r = 0

Solving
-5 + -3r = 0

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

Add '5' to each side of the equation.
-5 + 5 + -3r = 0 + 5

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

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

Divide each side by '-3'.
r = -1.666666667

Simplifying
r = -1.666666667
Subproblem 2
Set the factor '(1 + -3r)' equal to zero and attempt to solve:

Simplifying
1 + -3r = 0

Solving
1 + -3r = 0

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

Add '-1' to each side of the equation.
1 + -1 + -3r = 0 + -1

Combine like terms: 1 + -1 = 0
0 + -3r = 0 + -1
-3r = 0 + -1

Combine like terms: 0 + -1 = -1
-3r = -1

Divide each side by '-3'.
r = 0.3333333333

Simplifying
r = 0.3333333333
Solution
r = {-1.666666667, 0.3333333333}