(x-5)(x-7)=3

Solution for (x-5)(x-7)=3 equation:

Simplifying
(x + -5)(x + -7) = 3

Reorder the terms:
(-5 + x)(x + -7) = 3

Reorder the terms:
(-5 + x)(-7 + x) = 3

Multiply (-5 + x) * (-7 + x)
(-5(-7 + x) + x(-7 + x)) = 3
((-7 * -5 + x * -5) + x(-7 + x)) = 3
((35 + -5x) + x(-7 + x)) = 3
(35 + -5x + (-7 * x + x * x)) = 3
(35 + -5x + (-7x + x2)) = 3

Combine like terms: -5x + -7x = -12x
(35 + -12x + x2) = 3

Solving
35 + -12x + x2 = 3

Solving for variable 'x'.

Reorder the terms:
35 + -3 + -12x + x2 = 3 + -3

Combine like terms: 35 + -3 = 32
32 + -12x + x2 = 3 + -3

Combine like terms: 3 + -3 = 0
32 + -12x + x2 = 0

Factor a trinomial.
(4 + -1x)(8 + -1x) = 0

Subproblem 1
Set the factor '(4 + -1x)' equal to zero and attempt to solve:

Simplifying
4 + -1x = 0

Solving
4 + -1x = 0

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

Add '-4' to each side of the equation.
4 + -4 + -1x = 0 + -4

Combine like terms: 4 + -4 = 0
0 + -1x = 0 + -4
-1x = 0 + -4

Combine like terms: 0 + -4 = -4
-1x = -4

Divide each side by '-1'.
x = 4

Simplifying
x = 4
Subproblem 2
Set the factor '(8 + -1x)' equal to zero and attempt to solve:

Simplifying
8 + -1x = 0

Solving
8 + -1x = 0

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

Add '-8' to each side of the equation.
8 + -8 + -1x = 0 + -8

Combine like terms: 8 + -8 = 0
0 + -1x = 0 + -8
-1x = 0 + -8

Combine like terms: 0 + -8 = -8
-1x = -8

Divide each side by '-1'.
x = 8

Simplifying
x = 8
Solution
x = {4, 8}