(x-2)(x-4)=-1

Solution for (x-2)(x-4)=-1 equation:

Simplifying
(x + -2)(x + -4) = -1

Reorder the terms:
(-2 + x)(x + -4) = -1

Reorder the terms:
(-2 + x)(-4 + x) = -1

Multiply (-2 + x) * (-4 + x)
(-2(-4 + x) + x(-4 + x)) = -1
((-4 * -2 + x * -2) + x(-4 + x)) = -1
((8 + -2x) + x(-4 + x)) = -1
(8 + -2x + (-4 * x + x * x)) = -1
(8 + -2x + (-4x + x2)) = -1

Combine like terms: -2x + -4x = -6x
(8 + -6x + x2) = -1

Solving
8 + -6x + x2 = -1

Solving for variable 'x'.

Reorder the terms:
8 + 1 + -6x + x2 = -1 + 1

Combine like terms: 8 + 1 = 9
9 + -6x + x2 = -1 + 1

Combine like terms: -1 + 1 = 0
9 + -6x + x2 = 0

Factor a trinomial.
(3 + -1x)(3 + -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 '(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
Solution
x = {3, 3}