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

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

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

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

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

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

Combine like terms: -4x + -2x = -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}