2r^3+14r^2=36r

Solution for 2r^3+14r^2=36r equation:

Simplifying
2r3 + 14r2 = 36r

Reorder the terms:
14r2 + 2r3 = 36r

Solving
14r2 + 2r3 = 36r

Solving for variable 'r'.

Reorder the terms:
-36r + 14r2 + 2r3 = 36r + -36r

Combine like terms: 36r + -36r = 0
-36r + 14r2 + 2r3 = 0

Factor out the Greatest Common Factor (GCF), '2r'.
2r(-18 + 7r + r2) = 0

Factor a trinomial.
2r((-9 + -1r)(2 + -1r)) = 0

Ignore the factor 2.
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 '(-9 + -1r)' equal to zero and attempt to solve:

Simplifying
-9 + -1r = 0

Solving
-9 + -1r = 0

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

Add '9' to each side of the equation.
-9 + 9 + -1r = 0 + 9

Combine like terms: -9 + 9 = 0
0 + -1r = 0 + 9
-1r = 0 + 9

Combine like terms: 0 + 9 = 9
-1r = 9

Divide each side by '-1'.
r = -9

Simplifying
r = -9
Subproblem 3
Set the factor '(2 + -1r)' equal to zero and attempt to solve:

Simplifying
2 + -1r = 0

Solving
2 + -1r = 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 + -1r = 0 + -2

Combine like terms: 2 + -2 = 0
0 + -1r = 0 + -2
-1r = 0 + -2

Combine like terms: 0 + -2 = -2
-1r = -2

Divide each side by '-1'.
r = 2

Simplifying
r = 2
Solution
r = {0, -9, 2}