(x-3)(1-x)=1

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

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

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

Multiply (-3 + x) * (1 + -1x)
(-3(1 + -1x) + x(1 + -1x)) = 1
((1 * -3 + -1x * -3) + x(1 + -1x)) = 1
((-3 + 3x) + x(1 + -1x)) = 1
(-3 + 3x + (1 * x + -1x * x)) = 1
(-3 + 3x + (1x + -1x2)) = 1

Combine like terms: 3x + 1x = 4x
(-3 + 4x + -1x2) = 1

Solving
-3 + 4x + -1x2 = 1

Solving for variable 'x'.

Reorder the terms:
-3 + -1 + 4x + -1x2 = 1 + -1

Combine like terms: -3 + -1 = -4
-4 + 4x + -1x2 = 1 + -1

Combine like terms: 1 + -1 = 0
-4 + 4x + -1x2 = 0

Factor a trinomial.
(-2 + x)(2 + -1x) = 0

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

Simplifying
-2 + x = 0

Solving
-2 + x = 0

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

Add '2' to each side of the equation.
-2 + 2 + x = 0 + 2

Combine like terms: -2 + 2 = 0
0 + x = 0 + 2
x = 0 + 2

Combine like terms: 0 + 2 = 2
x = 2

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

Simplifying
2 + -1x = 0

Solving
2 + -1x = 0

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

Add '-2' to each side of the equation.
2 + -2 + -1x = 0 + -2

Combine like terms: 2 + -2 = 0
0 + -1x = 0 + -2
-1x = 0 + -2

Combine like terms: 0 + -2 = -2
-1x = -2

Divide each side by '-1'.
x = 2

Simplifying
x = 2
Solution
x = {2, 2}