(p-1)(p^2+p+1)=0

Solution for (p-1)(p^2+p+1)=0 equation:

Simplifying
(p + -1)(p2 + p + 1) = 0

Reorder the terms:
(-1 + p)(p2 + p + 1) = 0

Reorder the terms:
(-1 + p)(1 + p + p2) = 0

Multiply (-1 + p) * (1 + p + p2)
(-1(1 + p + p2) + p(1 + p + p2)) = 0
((1 * -1 + p * -1 + p2 * -1) + p(1 + p + p2)) = 0
((-1 + -1p + -1p2) + p(1 + p + p2)) = 0
(-1 + -1p + -1p2 + (1 * p + p * p + p2 * p)) = 0
(-1 + -1p + -1p2 + (1p + p2 + p3)) = 0

Reorder the terms:
(-1 + -1p + 1p + -1p2 + p2 + p3) = 0

Combine like terms: -1p + 1p = 0
(-1 + 0 + -1p2 + p2 + p3) = 0
(-1 + -1p2 + p2 + p3) = 0

Combine like terms: -1p2 + p2 = 0
(-1 + 0 + p3) = 0
(-1 + p3) = 0

Solving
-1 + p3 = 0

Solving for variable 'p'.

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

Add '1' to each side of the equation.
-1 + 1 + p3 = 0 + 1

Combine like terms: -1 + 1 = 0
0 + p3 = 0 + 1
p3 = 0 + 1

Combine like terms: 0 + 1 = 1
p3 = 1

Simplifying
p3 = 1

Reorder the terms:
-1 + p3 = 1 + -1

Combine like terms: 1 + -1 = 0
-1 + p3 = 0

The solution to this equation could not be determined.