r^4+2r^3+35r^2=0

Solution for r^4+2r^3+35r^2=0 equation:

Simplifying
r4 + 2r3 + 35r2 = 0

Reorder the terms:
35r2 + 2r3 + r4 = 0

Solving
35r2 + 2r3 + r4 = 0

Solving for variable 'r'.

Factor out the Greatest Common Factor (GCF), 'r2'.
r2(35 + 2r + r2) = 0

Subproblem 1
Set the factor 'r2' equal to zero and attempt to solve:

Simplifying
r2 = 0

Solving
r2 = 0

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

Simplifying
r2 = 0

Take the square root of each side:
r = {0}
Subproblem 2
Set the factor '(35 + 2r + r2)' equal to zero and attempt to solve:

Simplifying
35 + 2r + r2 = 0

Solving
35 + 2r + r2 = 0

Begin completing the square.

Move the constant term to the right:

Add '-35' to each side of the equation.
35 + 2r + -35 + r2 = 0 + -35

Reorder the terms:
35 + -35 + 2r + r2 = 0 + -35

Combine like terms: 35 + -35 = 0
0 + 2r + r2 = 0 + -35
2r + r2 = 0 + -35

Combine like terms: 0 + -35 = -35
2r + r2 = -35

The r term is 2r.  Take half its coefficient (1).
Square it (1) and add it to both sides.

Add '1' to each side of the equation.
2r + 1 + r2 = -35 + 1

Reorder the terms:
1 + 2r + r2 = -35 + 1

Combine like terms: -35 + 1 = -34
1 + 2r + r2 = -34

Factor a perfect square on the left side:
(r + 1)(r + 1) = -34

Can't calculate square root of the right side.

The solution to this equation could not be determined.

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