r^4+4r^3-21r^2=

Solution for r^4+4r^3-21r^2= equation:

Simplifying
r4 + 4r3 + -21r2 = 0

Reorder the terms:
-21r2 + 4r3 + r4 = 0

Solving
-21r2 + 4r3 + r4 = 0

Solving for variable 'r'.

Factor out the Greatest Common Factor (GCF), 'r2'.
r2(-21 + 4r + r2) = 0

Factor a trinomial.
r2((-7 + -1r)(3 + -1r)) = 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 '(-7 + -1r)' equal to zero and attempt to solve:

Simplifying
-7 + -1r = 0

Solving
-7 + -1r = 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 + -1r = 0 + 7

Combine like terms: -7 + 7 = 0
0 + -1r = 0 + 7
-1r = 0 + 7

Combine like terms: 0 + 7 = 7
-1r = 7

Divide each side by '-1'.
r = -7

Simplifying
r = -7
Subproblem 3
Set the factor '(3 + -1r)' equal to zero and attempt to solve:

Simplifying
3 + -1r = 0

Solving
3 + -1r = 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 + -1r = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -1r = 0 + -3
-1r = 0 + -3

Combine like terms: 0 + -3 = -3
-1r = -3

Divide each side by '-1'.
r = 3

Simplifying
r = 3
Solution
r = {0, -7, 3}