45r^2+15r-12=27r

Solution for 45r^2+15r-12=27r equation:

Simplifying
45r2 + 15r + -12 = 27r

Reorder the terms:
-12 + 15r + 45r2 = 27r

Solving
-12 + 15r + 45r2 = 27r

Solving for variable 'r'.

Reorder the terms:
-12 + 15r + -27r + 45r2 = 27r + -27r

Combine like terms: 15r + -27r = -12r
-12 + -12r + 45r2 = 27r + -27r

Combine like terms: 27r + -27r = 0
-12 + -12r + 45r2 = 0

Factor out the Greatest Common Factor (GCF), '3'.
3(-4 + -4r + 15r2) = 0

Factor a trinomial.
3((-2 + -5r)(2 + -3r)) = 0

Ignore the factor 3.
Subproblem 1
Set the factor '(-2 + -5r)' equal to zero and attempt to solve:

Simplifying
-2 + -5r = 0

Solving
-2 + -5r = 0

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

Add '2' to each side of the equation.
-2 + 2 + -5r = 0 + 2

Combine like terms: -2 + 2 = 0
0 + -5r = 0 + 2
-5r = 0 + 2

Combine like terms: 0 + 2 = 2
-5r = 2

Divide each side by '-5'.
r = -0.4

Simplifying
r = -0.4
Subproblem 2
Set the factor '(2 + -3r)' equal to zero and attempt to solve:

Simplifying
2 + -3r = 0

Solving
2 + -3r = 0

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

Add '-2' to each side of the equation.
2 + -2 + -3r = 0 + -2

Combine like terms: 2 + -2 = 0
0 + -3r = 0 + -2
-3r = 0 + -2

Combine like terms: 0 + -2 = -2
-3r = -2

Divide each side by '-3'.
r = 0.6666666667

Simplifying
r = 0.6666666667
Solution
r = {-0.4, 0.6666666667}