30r^3+55r^2-175r=

Solution for 30r^3+55r^2-175r= equation:

Simplifying
30r3 + 55r2 + -175r = 0

Reorder the terms:
-175r + 55r2 + 30r3 = 0

Solving
-175r + 55r2 + 30r3 = 0

Solving for variable 'r'.

Factor out the Greatest Common Factor (GCF), '5r'.
5r(-35 + 11r + 6r2) = 0

Factor a trinomial.
5r((-7 + -2r)(5 + -3r)) = 0

Ignore the factor 5.
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 '(-7 + -2r)' equal to zero and attempt to solve:

Simplifying
-7 + -2r = 0

Solving
-7 + -2r = 0

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

Add '7' to each side of the equation.
-7 + 7 + -2r = 0 + 7

Combine like terms: -7 + 7 = 0
0 + -2r = 0 + 7
-2r = 0 + 7

Combine like terms: 0 + 7 = 7
-2r = 7

Divide each side by '-2'.
r = -3.5

Simplifying
r = -3.5
Subproblem 3
Set the factor '(5 + -3r)' equal to zero and attempt to solve:

Simplifying
5 + -3r = 0

Solving
5 + -3r = 0

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

Add '-5' to each side of the equation.
5 + -5 + -3r = 0 + -5

Combine like terms: 5 + -5 = 0
0 + -3r = 0 + -5
-3r = 0 + -5

Combine like terms: 0 + -5 = -5
-3r = -5

Divide each side by '-3'.
r = 1.666666667

Simplifying
r = 1.666666667
Solution
r = {0, -3.5, 1.666666667}