(x-1)*(x-2(x-3))=1(1-x)

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

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

Reorder the terms:
(-1 + x)(x + -2(x + -3)) = 1(1 + -1x)

Reorder the terms:
(-1 + x)(x + -2(-3 + x)) = 1(1 + -1x)
(-1 + x)(x + (-3 * -2 + x * -2)) = 1(1 + -1x)
(-1 + x)(x + (6 + -2x)) = 1(1 + -1x)

Reorder the terms:
(-1 + x)(6 + x + -2x) = 1(1 + -1x)

Combine like terms: x + -2x = -1x
(-1 + x)(6 + -1x) = 1(1 + -1x)

Multiply (-1 + x) * (6 + -1x)
(-1(6 + -1x) + x(6 + -1x)) = 1(1 + -1x)
((6 * -1 + -1x * -1) + x(6 + -1x)) = 1(1 + -1x)
((-6 + 1x) + x(6 + -1x)) = 1(1 + -1x)
(-6 + 1x + (6 * x + -1x * x)) = 1(1 + -1x)
(-6 + 1x + (6x + -1x2)) = 1(1 + -1x)

Combine like terms: 1x + 6x = 7x
(-6 + 7x + -1x2) = 1(1 + -1x)
-6 + 7x + -1x2 = (1 * 1 + -1x * 1)
-6 + 7x + -1x2 = (1 + -1x)

Solving
-6 + 7x + -1x2 = 1 + -1x

Solving for variable 'x'.

Reorder the terms:
-6 + -1 + 7x + x + -1x2 = 1 + -1x + -1 + x

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

Combine like terms: 7x + x = 8x
-7 + 8x + -1x2 = 1 + -1x + -1 + x

Reorder the terms:
-7 + 8x + -1x2 = 1 + -1 + -1x + x

Combine like terms: 1 + -1 = 0
-7 + 8x + -1x2 = 0 + -1x + x
-7 + 8x + -1x2 = -1x + x

Combine like terms: -1x + x = 0
-7 + 8x + -1x2 = 0

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

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

Simplifying
-7 + x = 0

Solving
-7 + x = 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 + x = 0 + 7

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

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

Simplifying
x = 7
Subproblem 2
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
Solution
x = {7, 1}