(5x^3-5)=5(x-1)(x^2+x+1)

Solution for (5x^3-5)=5(x-1)(x^2+x+1) equation:

Simplifying
(5x3 + -5) = 5(x + -1)(x2 + x + 1)

Reorder the terms:
(-5 + 5x3) = 5(x + -1)(x2 + x + 1)

Remove parenthesis around (-5 + 5x3)
-5 + 5x3 = 5(x + -1)(x2 + x + 1)

Reorder the terms:
-5 + 5x3 = 5(-1 + x)(x2 + x + 1)

Reorder the terms:
-5 + 5x3 = 5(-1 + x)(1 + x + x2)

Multiply (-1 + x) * (1 + x + x2)
-5 + 5x3 = 5(-1(1 + x + x2) + x(1 + x + x2))
-5 + 5x3 = 5((1 * -1 + x * -1 + x2 * -1) + x(1 + x + x2))
-5 + 5x3 = 5((-1 + -1x + -1x2) + x(1 + x + x2))
-5 + 5x3 = 5(-1 + -1x + -1x2 + (1 * x + x * x + x2 * x))
-5 + 5x3 = 5(-1 + -1x + -1x2 + (1x + x2 + x3))

Reorder the terms:
-5 + 5x3 = 5(-1 + -1x + 1x + -1x2 + x2 + x3)

Combine like terms: -1x + 1x = 0
-5 + 5x3 = 5(-1 + 0 + -1x2 + x2 + x3)
-5 + 5x3 = 5(-1 + -1x2 + x2 + x3)

Combine like terms: -1x2 + x2 = 0
-5 + 5x3 = 5(-1 + 0 + x3)
-5 + 5x3 = 5(-1 + x3)
-5 + 5x3 = (-1 * 5 + x3 * 5)
-5 + 5x3 = (-5 + 5x3)

Add '5' to each side of the equation.
-5 + 5 + 5x3 = -5 + 5 + 5x3

Combine like terms: -5 + 5 = 0
0 + 5x3 = -5 + 5 + 5x3
5x3 = -5 + 5 + 5x3

Combine like terms: -5 + 5 = 0
5x3 = 0 + 5x3
5x3 = 5x3

Add '-5x3' to each side of the equation.
5x3 + -5x3 = 5x3 + -5x3

Combine like terms: 5x3 + -5x3 = 0
0 = 5x3 + -5x3

Combine like terms: 5x3 + -5x3 = 0
0 = 0

Solving
0 = 0

Couldn't find a variable to solve for.

This equation is an identity, all real numbers are solutions.