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

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

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

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

Reorder the terms:
-1x + -1x2 + x3 + -1x3 = 1 + -1x2

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

Add 'x2' to each side of the equation.
-1x + -1x2 + x2 = 1 + -1x2 + x2

Combine like terms: -1x2 + x2 = 0
-1x + 0 = 1 + -1x2 + x2
-1x = 1 + -1x2 + x2

Combine like terms: -1x2 + x2 = 0
-1x = 1 + 0
-1x = 1

Solving
-1x = 1

Solving for variable 'x'.

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

Divide each side by '-1'.
x = -1

Simplifying
x = -1