9r^3+45r^2=54r

Solution for 9r^3+45r^2=54r equation:

Simplifying
9r3 + 45r2 = 54r

Reorder the terms:
45r2 + 9r3 = 54r

Solving
45r2 + 9r3 = 54r

Solving for variable 'r'.

Reorder the terms:
-54r + 45r2 + 9r3 = 54r + -54r

Combine like terms: 54r + -54r = 0
-54r + 45r2 + 9r3 = 0

Factor out the Greatest Common Factor (GCF), '9r'.
9r(-6 + 5r + r2) = 0

Factor a trinomial.
9r((-6 + -1r)(1 + -1r)) = 0

Ignore the factor 9.
Subproblem 1
Set the factor 'r' equal to zero and attempt to solve:

Simplifying
r = 0

Solving
r = 0

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

Simplifying
r = 0
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
Subproblem 3
Set the factor '(1 + -1r)' equal to zero and attempt to solve:

Simplifying
1 + -1r = 0

Solving
1 + -1r = 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 + -1r = 0 + -1

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

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

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

Simplifying
r = 1
Solution
r = {0, -6, 1}