(x-7)(x-5)=-1

Solution for (x-7)(x-5)=-1 equation:

Simplifying
(x + -7)(x + -5) = -1

Reorder the terms:
(-7 + x)(x + -5) = -1

Reorder the terms:
(-7 + x)(-5 + x) = -1

Multiply (-7 + x) * (-5 + x)
(-7(-5 + x) + x(-5 + x)) = -1
((-5 * -7 + x * -7) + x(-5 + x)) = -1
((35 + -7x) + x(-5 + x)) = -1
(35 + -7x + (-5 * x + x * x)) = -1
(35 + -7x + (-5x + x2)) = -1

Combine like terms: -7x + -5x = -12x
(35 + -12x + x2) = -1

Solving
35 + -12x + x2 = -1

Solving for variable 'x'.

Reorder the terms:
35 + 1 + -12x + x2 = -1 + 1

Combine like terms: 35 + 1 = 36
36 + -12x + x2 = -1 + 1

Combine like terms: -1 + 1 = 0
36 + -12x + x2 = 0

Factor a trinomial.
(6 + -1x)(6 + -1x) = 0

Subproblem 1
Set the factor '(6 + -1x)' equal to zero and attempt to solve:

Simplifying
6 + -1x = 0

Solving
6 + -1x = 0

Move all terms containing x to the left, all other terms to the right.

Add '-6' to each side of the equation.
6 + -6 + -1x = 0 + -6

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

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

Divide each side by '-1'.
x = 6

Simplifying
x = 6
Subproblem 2
Set the factor '(6 + -1x)' equal to zero and attempt to solve:

Simplifying
6 + -1x = 0

Solving
6 + -1x = 0

Move all terms containing x to the left, all other terms to the right.

Add '-6' to each side of the equation.
6 + -6 + -1x = 0 + -6

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

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

Divide each side by '-1'.
x = 6

Simplifying
x = 6
Solution
x = {6, 6}