w(x)=x[x^2-(m+1)+m]

Solution for w(x)=x[x^2-(m+1)+m] equation:

Simplifying
w(x) = x[x2 + -1(m + 1) + m]

Multiply w * x
wx = x[x2 + -1(m + 1) + m]

Reorder the terms:
wx = x[x2 + -1(1 + m) + m]
wx = x[x2 + (1 * -1 + m * -1) + m]
wx = x[x2 + (-1 + -1m) + m]

Reorder the terms:
wx = x[-1 + -1m + m + x2]

Combine like terms: -1m + m = 0
wx = x[-1 + 0 + x2]
wx = x[-1 + x2]
wx = [-1 * x + x2 * x]
wx = [-1x + x3]

Solving
wx = -1x + x3

Solving for variable 'w'.

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

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

Simplifying
w = -1 + x2