(x-9)(x-5)=5

Solution for (x-9)(x-5)=5 equation:

Simplifying
(x + -9)(x + -5) = 5

Reorder the terms:
(-9 + x)(x + -5) = 5

Reorder the terms:
(-9 + x)(-5 + x) = 5

Multiply (-9 + x) * (-5 + x)
(-9(-5 + x) + x(-5 + x)) = 5
((-5 * -9 + x * -9) + x(-5 + x)) = 5
((45 + -9x) + x(-5 + x)) = 5
(45 + -9x + (-5 * x + x * x)) = 5
(45 + -9x + (-5x + x2)) = 5

Combine like terms: -9x + -5x = -14x
(45 + -14x + x2) = 5

Solving
45 + -14x + x2 = 5

Solving for variable 'x'.

Reorder the terms:
45 + -5 + -14x + x2 = 5 + -5

Combine like terms: 45 + -5 = 40
40 + -14x + x2 = 5 + -5

Combine like terms: 5 + -5 = 0
40 + -14x + x2 = 0

Factor a trinomial.
(4 + -1x)(10 + -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 '(10 + -1x)' equal to zero and attempt to solve:

Simplifying
10 + -1x = 0

Solving
10 + -1x = 0

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

Add '-10' to each side of the equation.
10 + -10 + -1x = 0 + -10

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

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

Divide each side by '-1'.
x = 10

Simplifying
x = 10
Solution
x = {4, 10}