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

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

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

Reorder the terms:
(-1 + x)(3 + -1x) = -8

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

Combine like terms: 1x + 3x = 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.
(5 + -1x)(1 + x) = 0

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

Simplifying
1 + x = 0

Solving
1 + x = 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 + x = 0 + -1

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

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

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