h(x)=(x-1)(x^2+x+1)

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

Simplifying
h(x) = (x + -1)(x2 + x + 1)

Multiply h * x
hx = (x + -1)(x2 + x + 1)

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

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

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

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

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

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

Solving
hx = -1 + x3

Solving for variable 'h'.

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

Divide each side by 'x'.
h = -1x-1 + x2

Simplifying
h = -1x-1 + x2