(9+x)(13+x)-221=0

Solution for (9+x)(13+x)-221=0 equation:

Simplifying
(9 + x)(13 + x) + -221 = 0

Multiply (9 + x) * (13 + x)
(9(13 + x) + x(13 + x)) + -221 = 0
((13 * 9 + x * 9) + x(13 + x)) + -221 = 0
((117 + 9x) + x(13 + x)) + -221 = 0
(117 + 9x + (13 * x + x * x)) + -221 = 0
(117 + 9x + (13x + x2)) + -221 = 0

Combine like terms: 9x + 13x = 22x
(117 + 22x + x2) + -221 = 0

Reorder the terms:
117 + -221 + 22x + x2 = 0

Combine like terms: 117 + -221 = -104
-104 + 22x + x2 = 0

Solving
-104 + 22x + x2 = 0

Solving for variable 'x'.

Factor a trinomial.
(-26 + -1x)(4 + -1x) = 0

Subproblem 1
Set the factor '(-26 + -1x)' equal to zero and attempt to solve:

Simplifying
-26 + -1x = 0

Solving
-26 + -1x = 0

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

Add '26' to each side of the equation.
-26 + 26 + -1x = 0 + 26

Combine like terms: -26 + 26 = 0
0 + -1x = 0 + 26
-1x = 0 + 26

Combine like terms: 0 + 26 = 26
-1x = 26

Divide each side by '-1'.
x = -26

Simplifying
x = -26
Subproblem 2
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
Solution
x = {-26, 4}