10r^3=10r

Solution for 10r^3=10r equation:

Simplifying
10r3 = 10r

Solving
10r3 = 10r

Solving for variable 'r'.

Reorder the terms:
-10r + 10r3 = 10r + -10r

Combine like terms: 10r + -10r = 0
-10r + 10r3 = 0

Factor out the Greatest Common Factor (GCF), '10r'.
10r(-1 + r2) = 0

Factor a difference between two squares.
10r((1 + r)(-1 + r)) = 0

Ignore the factor 10.
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 '(1 + r)' equal to zero and attempt to solve:

Simplifying
1 + r = 0

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

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

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

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

Simplifying
-1 + r = 0

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

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

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

Simplifying
r = 1
Solution
r = {0, -1, 1}