(x-4)(x-6)=-1

Solution for (x-4)(x-6)=-1 equation:

Simplifying
(x + -4)(x + -6) = -1

Reorder the terms:
(-4 + x)(x + -6) = -1

Reorder the terms:
(-4 + x)(-6 + x) = -1

Multiply (-4 + x) * (-6 + x)
(-4(-6 + x) + x(-6 + x)) = -1
((-6 * -4 + x * -4) + x(-6 + x)) = -1
((24 + -4x) + x(-6 + x)) = -1
(24 + -4x + (-6 * x + x * x)) = -1
(24 + -4x + (-6x + x2)) = -1

Combine like terms: -4x + -6x = -10x
(24 + -10x + x2) = -1

Solving
24 + -10x + x2 = -1

Solving for variable 'x'.

Reorder the terms:
24 + 1 + -10x + x2 = -1 + 1

Combine like terms: 24 + 1 = 25
25 + -10x + x2 = -1 + 1

Combine like terms: -1 + 1 = 0
25 + -10x + x2 = 0

Factor a trinomial.
(5 + -1x)(5 + -1x) = 0

Subproblem 1
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
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 = {5, 5}