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

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

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

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

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

Multiply (-7 + x) * (-3 + x)
(-7(-3 + x) + x(-3 + x)) = 5
((-3 * -7 + x * -7) + x(-3 + x)) = 5
((21 + -7x) + x(-3 + x)) = 5
(21 + -7x + (-3 * x + x * x)) = 5
(21 + -7x + (-3x + x2)) = 5

Combine like terms: -7x + -3x = -10x
(21 + -10x + x2) = 5

Solving
21 + -10x + x2 = 5

Solving for variable 'x'.

Reorder the terms:
21 + -5 + -10x + x2 = 5 + -5

Combine like terms: 21 + -5 = 16
16 + -10x + x2 = 5 + -5

Combine like terms: 5 + -5 = 0
16 + -10x + x2 = 0

Factor a trinomial.
(2 + -1x)(8 + -1x) = 0

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

Simplifying
2 + -1x = 0

Solving
2 + -1x = 0

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

Add '-2' to each side of the equation.
2 + -2 + -1x = 0 + -2

Combine like terms: 2 + -2 = 0
0 + -1x = 0 + -2
-1x = 0 + -2

Combine like terms: 0 + -2 = -2
-1x = -2

Divide each side by '-1'.
x = 2

Simplifying
x = 2
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 = {2, 8}