112r^3+34r^2-6r=0

Solution for 112r^3+34r^2-6r=0 equation:

Simplifying
112r3 + 34r2 + -6r = 0

Reorder the terms:
-6r + 34r2 + 112r3 = 0

Solving
-6r + 34r2 + 112r3 = 0

Solving for variable 'r'.

Factor out the Greatest Common Factor (GCF), '2r'.
2r(-3 + 17r + 56r2) = 0

Factor a trinomial.
2r((-3 + -7r)(1 + -8r)) = 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 '(-3 + -7r)' equal to zero and attempt to solve:

Simplifying
-3 + -7r = 0

Solving
-3 + -7r = 0

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

Add '3' to each side of the equation.
-3 + 3 + -7r = 0 + 3

Combine like terms: -3 + 3 = 0
0 + -7r = 0 + 3
-7r = 0 + 3

Combine like terms: 0 + 3 = 3
-7r = 3

Divide each side by '-7'.
r = -0.4285714286

Simplifying
r = -0.4285714286
Subproblem 3
Set the factor '(1 + -8r)' equal to zero and attempt to solve:

Simplifying
1 + -8r = 0

Solving
1 + -8r = 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 + -8r = 0 + -1

Combine like terms: 1 + -1 = 0
0 + -8r = 0 + -1
-8r = 0 + -1

Combine like terms: 0 + -1 = -1
-8r = -1

Divide each side by '-8'.
r = 0.125

Simplifying
r = 0.125
Solution
r = {0, -0.4285714286, 0.125}