(3-x)(1-x)=8

Solution for (3-x)(1-x)=8 equation:

Simplifying
(3 + -1x)(1 + -1x) = 8

Multiply (3 + -1x) * (1 + -1x)
(3(1 + -1x) + -1x * (1 + -1x)) = 8
((1 * 3 + -1x * 3) + -1x * (1 + -1x)) = 8
((3 + -3x) + -1x * (1 + -1x)) = 8
(3 + -3x + (1 * -1x + -1x * -1x)) = 8
(3 + -3x + (-1x + 1x2)) = 8

Combine like terms: -3x + -1x = -4x
(3 + -4x + 1x2) = 8

Solving
3 + -4x + 1x2 = 8

Solving for variable 'x'.

Reorder the terms:
3 + -8 + -4x + 1x2 = 8 + -8

Combine like terms: 3 + -8 = -5
-5 + -4x + 1x2 = 8 + -8

Combine like terms: 8 + -8 = 0
-5 + -4x + 1x2 = 0

Factor a trinomial.
(-1 + -1x)(5 + -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 '(5 + -1x)' equal to zero and attempt to solve:

Simplifying
5 + -1x = 0

Solving
5 + -1x = 0

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

Add '-5' to each side of the equation.
5 + -5 + -1x = 0 + -5

Combine like terms: 5 + -5 = 0
0 + -1x = 0 + -5
-1x = 0 + -5

Combine like terms: 0 + -5 = -5
-1x = -5

Divide each side by '-1'.
x = 5

Simplifying
x = 5
Solution
x = {-1, 5}