27r^2-24r+36r-32=

Solution for 27r^2-24r+36r-32= equation:

Simplifying
27r2 + -24r + 36r + -32 = 0

Reorder the terms:
-32 + -24r + 36r + 27r2 = 0

Combine like terms: -24r + 36r = 12r
-32 + 12r + 27r2 = 0

Solving
-32 + 12r + 27r2 = 0

Solving for variable 'r'.

Factor a trinomial.
(-4 + -3r)(8 + -9r) = 0

Subproblem 1
Set the factor '(-4 + -3r)' equal to zero and attempt to solve:

Simplifying
-4 + -3r = 0

Solving
-4 + -3r = 0

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

Add '4' to each side of the equation.
-4 + 4 + -3r = 0 + 4

Combine like terms: -4 + 4 = 0
0 + -3r = 0 + 4
-3r = 0 + 4

Combine like terms: 0 + 4 = 4
-3r = 4

Divide each side by '-3'.
r = -1.333333333

Simplifying
r = -1.333333333
Subproblem 2
Set the factor '(8 + -9r)' equal to zero and attempt to solve:

Simplifying
8 + -9r = 0

Solving
8 + -9r = 0

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

Add '-8' to each side of the equation.
8 + -8 + -9r = 0 + -8

Combine like terms: 8 + -8 = 0
0 + -9r = 0 + -8
-9r = 0 + -8

Combine like terms: 0 + -8 = -8
-9r = -8

Divide each side by '-9'.
r = 0.8888888889

Simplifying
r = 0.8888888889
Solution
r = {-1.333333333, 0.8888888889}