(7+x)(11+x)=117

Solution for (7+x)(11+x)=117 equation:

Simplifying
(7 + x)(11 + x) = 117

Multiply (7 + x) * (11 + x)
(7(11 + x) + x(11 + x)) = 117
((11 * 7 + x * 7) + x(11 + x)) = 117
((77 + 7x) + x(11 + x)) = 117
(77 + 7x + (11 * x + x * x)) = 117
(77 + 7x + (11x + x2)) = 117

Combine like terms: 7x + 11x = 18x
(77 + 18x + x2) = 117

Solving
77 + 18x + x2 = 117

Solving for variable 'x'.

Reorder the terms:
77 + -117 + 18x + x2 = 117 + -117

Combine like terms: 77 + -117 = -40
-40 + 18x + x2 = 117 + -117

Combine like terms: 117 + -117 = 0
-40 + 18x + x2 = 0

Factor a trinomial.
(-20 + -1x)(2 + -1x) = 0

Subproblem 1
Set the factor '(-20 + -1x)' equal to zero and attempt to solve:

Simplifying
-20 + -1x = 0

Solving
-20 + -1x = 0

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

Add '20' to each side of the equation.
-20 + 20 + -1x = 0 + 20

Combine like terms: -20 + 20 = 0
0 + -1x = 0 + 20
-1x = 0 + 20

Combine like terms: 0 + 20 = 20
-1x = 20

Divide each side by '-1'.
x = -20

Simplifying
x = -20
Subproblem 2
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
Solution
x = {-20, 2}