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

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

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

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

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

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

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

Solving
32 = 5 + -6x + x2

Solving for variable 'x'.

Combine like terms: 32 + -5 = 27
27 + 6x + -1x2 = 5 + -6x + x2 + -5 + 6x + -1x2

Reorder the terms:
27 + 6x + -1x2 = 5 + -5 + -6x + 6x + x2 + -1x2

Combine like terms: 5 + -5 = 0
27 + 6x + -1x2 = 0 + -6x + 6x + x2 + -1x2
27 + 6x + -1x2 = -6x + 6x + x2 + -1x2

Combine like terms: -6x + 6x = 0
27 + 6x + -1x2 = 0 + x2 + -1x2
27 + 6x + -1x2 = x2 + -1x2

Combine like terms: x2 + -1x2 = 0
27 + 6x + -1x2 = 0

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

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

Simplifying
3 + x = 0

Solving
3 + x = 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 + x = 0 + -3

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

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

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