[(x-2)-5][(x-2)+3]=0

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Solution for [(x-2)-5][(x-2)+3]=0 equation: 


Simplifying
[(x + -2) + -5][(x + -2) + 3] = 0

Reorder the terms:
[(-2 + x) + -5][(x + -2) + 3] = 0

Remove parenthesis around (-2 + x)
[-2 + x + -5][(x + -2) + 3] = 0

Reorder the terms:
[-2 + -5 + x][(x + -2) + 3] = 0

Combine like terms: -2 + -5 = -7
[-7 + x][(x + -2) + 3] = 0

Reorder the terms:
[-7 + x][(-2 + x) + 3] = 0

Remove parenthesis around (-2 + x)
[-7 + x][-2 + x + 3] = 0

Reorder the terms:
[-7 + x][-2 + 3 + x] = 0

Combine like terms: -2 + 3 = 1
[-7 + x][1 + x] = 0

Multiply [-7 + x] * [1 + x]
[-7[1 + x] + x[1 + x]] = 0
[[1 * -7 + x * -7] + x[1 + x]] = 0
[[-7 + -7x] + x[1 + x]] = 0
[-7 + -7x + [1 * x + x * x]] = 0
[-7 + -7x + [1x + x2]] = 0

Combine like terms: -7x + 1x = -6x
[-7 + -6x + x2] = 0

Solving
-7 + -6x + x2 = 0

Solving for variable 'x'.

Factor a trinomial.
(-1 + -1x)(7 + -1x) = 0


Subproblem 1
Set the factor '(-1 + -1x)' equal to zero and attempt to solve:

Simplifying
-1 + -1x = 0

Solving
-1 + -1x = 0

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

Add '1' to each side of the equation.
-1 + 1 + -1x = 0 + 1

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

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

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

Simplifying
x = -1

Subproblem 2
Set the factor '(7 + -1x)' equal to zero and attempt to solve:

Simplifying
7 + -1x = 0

Solving
7 + -1x = 0

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

Add '-7' to each side of the equation.
7 + -7 + -1x = 0 + -7

Combine like terms: 7 + -7 = 0
0 + -1x = 0 + -7
-1x = 0 + -7

Combine like terms: 0 + -7 = -7
-1x = -7

Divide each side by '-1'.
x = 7

Simplifying
x = 7
Solution
x = {-1, 7}

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