(x-5)(x-1)=32

Solution for (x-5)(x-1)=32 equation:

Simplifying
(x + -5)(x + -1) = 32

Reorder the terms:
(-5 + x)(x + -1) = 32

Reorder the terms:
(-5 + x)(-1 + x) = 32

Multiply (-5 + x) * (-1 + x)
(-5(-1 + x) + x(-1 + x)) = 32
((-1 * -5 + x * -5) + x(-1 + x)) = 32
((5 + -5x) + x(-1 + x)) = 32
(5 + -5x + (-1 * x + x * x)) = 32
(5 + -5x + (-1x + x2)) = 32

Combine like terms: -5x + -1x = -6x
(5 + -6x + x2) = 32

Solving
5 + -6x + x2 = 32

Solving for variable 'x'.

Reorder the terms:
5 + -32 + -6x + x2 = 32 + -32

Combine like terms: 5 + -32 = -27
-27 + -6x + x2 = 32 + -32

Combine like terms: 32 + -32 = 0
-27 + -6x + x2 = 0

Factor a trinomial.
(-3 + -1x)(9 + -1x) = 0

Subproblem 1
Set the factor '(-3 + -1x)' equal to zero and attempt to solve:

Simplifying
-3 + -1x = 0

Solving
-3 + -1x = 0

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

Add '3' to each side of the equation.
-3 + 3 + -1x = 0 + 3

Combine like terms: -3 + 3 = 0
0 + -1x = 0 + 3
-1x = 0 + 3

Combine like terms: 0 + 3 = 3
-1x = 3

Divide each side by '-1'.
x = -3

Simplifying
x = -3
Subproblem 2
Set the factor '(9 + -1x)' equal to zero and attempt to solve:

Simplifying
9 + -1x = 0

Solving
9 + -1x = 0

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

Add '-9' to each side of the equation.
9 + -9 + -1x = 0 + -9

Combine like terms: 9 + -9 = 0
0 + -1x = 0 + -9
-1x = 0 + -9

Combine like terms: 0 + -9 = -9
-1x = -9

Divide each side by '-1'.
x = 9

Simplifying
x = 9
Solution
x = {-3, 9}