(6+x)(9+x)=88

Solution for (6+x)(9+x)=88 equation:

Simplifying
(6 + x)(9 + x) = 88

Multiply (6 + x) * (9 + x)
(6(9 + x) + x(9 + x)) = 88
((9 * 6 + x * 6) + x(9 + x)) = 88
((54 + 6x) + x(9 + x)) = 88
(54 + 6x + (9 * x + x * x)) = 88
(54 + 6x + (9x + x2)) = 88

Combine like terms: 6x + 9x = 15x
(54 + 15x + x2) = 88

Solving
54 + 15x + x2 = 88

Solving for variable 'x'.

Reorder the terms:
54 + -88 + 15x + x2 = 88 + -88

Combine like terms: 54 + -88 = -34
-34 + 15x + x2 = 88 + -88

Combine like terms: 88 + -88 = 0
-34 + 15x + x2 = 0

Factor a trinomial.
(-17 + -1x)(2 + -1x) = 0

Subproblem 1
Set the factor '(-17 + -1x)' equal to zero and attempt to solve:

Simplifying
-17 + -1x = 0

Solving
-17 + -1x = 0

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

Add '17' to each side of the equation.
-17 + 17 + -1x = 0 + 17

Combine like terms: -17 + 17 = 0
0 + -1x = 0 + 17
-1x = 0 + 17

Combine like terms: 0 + 17 = 17
-1x = 17

Divide each side by '-1'.
x = -17

Simplifying
x = -17
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 = {-17, 2}