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1) To solve the equation 1((x-3)(x+2)-(x-x-3)^2=0, we can simplify it step by step:

1((x-3)(x+2)-(x-x-3)^2=0
(x-3)(x+2)-(x-x-3)^2=0
(x-3)(x+2)-(0-3)^2=0
(x-3)(x+2)-9=0
(x^2-x-6)-9=0
x^2-x-15=0

Now we have a quadratic equation. We can solve it by factoring or using the quadratic formula.

Factoring:
(x-5)(x+3)=0

Setting each factor equal to zero:
x-5=0 or x+3=0

Solving for x:
x=5 or x=-3

So the solutions to the equation are x=5 and x=-3.

2) To solve the equation (2x-2)(2x+2)-4(x^2-3x+1)=0, we can simplify it step by step:

(2x-2)(2x+2)-4(x^2-3x+1)=0
4x^2-4-4x^2+12x-4=0
8x-8=0

Dividing both sides by 8:
x-1=0

Solving for x:
x=1

So the solution to the equation is x=1.

3) To solve the equation 7x(x-2)=(x-2), we can simplify it step by step:

7x(x-2)=(x-2)
7x^2-14x=x-2
7x^2-14x-x+2=0
7x^2-15x+2=0

Now we have a quadratic equation. We can solve it by factoring or using the quadratic formula.

Factoring:
(7x-1)(x-2)=0

Setting each factor equal to zero:
7x-1=0 or x-2=0

Solving for x:
7x=1 or x=2

Dividing both sides by 7:
x=1/7

So the solutions to the equation are x=1/7 and x=2.

4) To solve the equation 2x(x+2)-x^2-2x=0, we can simplify it step by step:

2x(x+2)-x^2-2x=0
2x^2+4x-x^2-2x=0
x^2+2x=0

Now we have a quadratic equation. We can solve it by factoring or using the quadratic formula.

Factoring:
x(x+2)=0

Setting each factor equal to zero:
x=0 or x+2=0

Solving for x:
x=0 or x=-2

So the solutions to the equation are x=0 and x=-2.