Question 647919
I think this is what you meant when posting your problem: {{{(x-1)^2 - (x+1)^2=4}}}

Firstly, we must rewrite this problem so it is easier to understand.

Step 1: Rewrite the problem without having to use powers

{{{(x-1)^2 - (x+1)^2=4}}}
{{{(x-1)(x-1) - (x+1)(x+1)=4}}}

Step 2: Distribute the left side parenthesis

{{{(x-1)(x-1) - (x+1)(x+1)=4}}}
{{{(x^2 - x - x +1) - (x+1)(x+1)=4}}}

Step 3: Distribute the right side parenthesis

{{{(x^2 - x - x +1) - (x^2 + x + x + 1)=4}}}

Step 4: Combine like terms

{{{(x^2 - x - x +1) - (x^2 + x + x + 1)=4}}}
{{{(x^2 - 2x +1) - (x^2 + 2x + 1)=4}}}

Step 4: Continue combining like terms

{{{(x^2 - 2x +1) - (x^2 + 2x + 1)=4}}}

All of the terms cancel out, giving you 0

What you get: 0 = 4

This means that this equation is inconsistent, meaning that there are no solutions for this system.

0 cannot be equal to 4.
The answer is no solution.