5r^4-3125=

Solution for 5r^4-3125= equation:

Simplifying
5r4 + -3125 = 0

Reorder the terms:
-3125 + 5r4 = 0

Solving
-3125 + 5r4 = 0

Solving for variable 'r'.

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

Add '3125' to each side of the equation.
-3125 + 3125 + 5r4 = 0 + 3125

Combine like terms: -3125 + 3125 = 0
0 + 5r4 = 0 + 3125
5r4 = 0 + 3125

Combine like terms: 0 + 3125 = 3125
5r4 = 3125

Divide each side by '5'.
r4 = 625

Simplifying
r4 = 625

Reorder the terms:
-625 + r4 = 625 + -625

Combine like terms: 625 + -625 = 0
-625 + r4 = 0

Factor a difference between two squares.
(25 + r2)(-25 + r2) = 0

Factor a difference between two squares.
(25 + r2)((5 + r)(-5 + r)) = 0

Subproblem 1
Set the factor '(25 + r2)' equal to zero and attempt to solve:

Simplifying
25 + r2 = 0

Solving
25 + r2 = 0

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

Add '-25' to each side of the equation.
25 + -25 + r2 = 0 + -25

Combine like terms: 25 + -25 = 0
0 + r2 = 0 + -25
r2 = 0 + -25

Combine like terms: 0 + -25 = -25
r2 = -25

Simplifying
r2 = -25

The solution to this equation could not be determined.

This subproblem is being ignored because a solution could not be determined.
Subproblem 2
Set the factor '(5 + r)' equal to zero and attempt to solve:

Simplifying
5 + r = 0

Solving
5 + r = 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 + r = 0 + -5

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

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

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

Simplifying
-5 + r = 0

Solving
-5 + r = 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 + r = 0 + 5

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

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

Simplifying
r = 5
Solution
r = {-5, 5}