1(x+1)+x(x-1)=1

Solution for 1(x+1)+x(x-1)=1 equation:

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

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

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

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

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

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

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

Solving
x2 = 0

Solving for variable 'x'.

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

Simplifying
x2 = 0

Take the square root of each side:
x = {0}