F(r)=5r+2r^3-3r-7r^3

Solution for F(r)=5r+2r^3-3r-7r^3 equation:

Simplifying
F(r) = 5r + 2r3 + -3r + -7r3

Multiply F * r
rF = 5r + 2r3 + -3r + -7r3

Reorder the terms:
rF = 5r + -3r + 2r3 + -7r3

Combine like terms: 5r + -3r = 2r
rF = 2r + 2r3 + -7r3

Combine like terms: 2r3 + -7r3 = -5r3
rF = 2r + -5r3

Solving
rF = 2r + -5r3

Solving for variable 'r'.

Reorder the terms:
-2r + rF + 5r3 = 2r + -5r3 + -2r + 5r3

Reorder the terms:
-2r + rF + 5r3 = 2r + -2r + -5r3 + 5r3

Combine like terms: 2r + -2r = 0
-2r + rF + 5r3 = 0 + -5r3 + 5r3
-2r + rF + 5r3 = -5r3 + 5r3

Combine like terms: -5r3 + 5r3 = 0
-2r + rF + 5r3 = 0

Factor out the Greatest Common Factor (GCF), 'r'.
r(-2 + F + 5r2) = 0

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 '(-2 + F + 5r2)' equal to zero and attempt to solve:

Simplifying
-2 + F + 5r2 = 0

Solving
-2 + F + 5r2 = 0

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

Add '2' to each side of the equation.
-2 + F + 2 + 5r2 = 0 + 2

Reorder the terms:
-2 + 2 + F + 5r2 = 0 + 2

Combine like terms: -2 + 2 = 0
0 + F + 5r2 = 0 + 2
F + 5r2 = 0 + 2

Combine like terms: 0 + 2 = 2
F + 5r2 = 2

Add '-1F' to each side of the equation.
F + -1F + 5r2 = 2 + -1F

Combine like terms: F + -1F = 0
0 + 5r2 = 2 + -1F
5r2 = 2 + -1F

Divide each side by '5'.
r2 = 0.4 + -0.2F

Simplifying
r2 = 0.4 + -0.2F

The solution to this equation could not be determined.

This subproblem is being ignored because a solution could not be determined.
Solution
r = {0}