-27r^2-21r+10=0

Solution for -27r^2-21r+10=0 equation:

Simplifying
-27r2 + -21r + 10 = 0

Reorder the terms:
10 + -21r + -27r2 = 0

Solving
10 + -21r + -27r2 = 0

Solving for variable 'r'.

Factor a trinomial.
(1 + -3r)(10 + 9r) = 0

Subproblem 1
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
Subproblem 2
Set the factor '(10 + 9r)' equal to zero and attempt to solve:

Simplifying
10 + 9r = 0

Solving
10 + 9r = 0

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

Add '-10' to each side of the equation.
10 + -10 + 9r = 0 + -10

Combine like terms: 10 + -10 = 0
0 + 9r = 0 + -10
9r = 0 + -10

Combine like terms: 0 + -10 = -10
9r = -10

Divide each side by '9'.
r = -1.111111111

Simplifying
r = -1.111111111
Solution
r = {0.3333333333, -1.111111111}