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

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


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

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

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

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

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

Solving
3 + -4x + x2 = 8

Solving for variable 'x'.

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

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

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

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