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

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

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

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

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

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

Combine like terms: -6x + -4x = -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}