(5+x)(6+x)-72=0

Solution for (5+x)(6+x)-72=0 equation:

Simplifying
(5 + x)(6 + x) + -72 = 0

Multiply (5 + x) * (6 + x)
(5(6 + x) + x(6 + x)) + -72 = 0
((6 * 5 + x * 5) + x(6 + x)) + -72 = 0
((30 + 5x) + x(6 + x)) + -72 = 0
(30 + 5x + (6 * x + x * x)) + -72 = 0
(30 + 5x + (6x + x2)) + -72 = 0

Combine like terms: 5x + 6x = 11x
(30 + 11x + x2) + -72 = 0

Reorder the terms:
30 + -72 + 11x + x2 = 0

Combine like terms: 30 + -72 = -42
-42 + 11x + x2 = 0

Solving
-42 + 11x + x2 = 0

Solving for variable 'x'.

Factor a trinomial.
(-14 + -1x)(3 + -1x) = 0

Subproblem 1
Set the factor '(-14 + -1x)' equal to zero and attempt to solve:

Simplifying
-14 + -1x = 0

Solving
-14 + -1x = 0

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

Add '14' to each side of the equation.
-14 + 14 + -1x = 0 + 14

Combine like terms: -14 + 14 = 0
0 + -1x = 0 + 14
-1x = 0 + 14

Combine like terms: 0 + 14 = 14
-1x = 14

Divide each side by '-1'.
x = -14

Simplifying
x = -14
Subproblem 2
Set the factor '(3 + -1x)' equal to zero and attempt to solve:

Simplifying
3 + -1x = 0

Solving
3 + -1x = 0

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

Add '-3' to each side of the equation.
3 + -3 + -1x = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -1x = 0 + -3
-1x = 0 + -3

Combine like terms: 0 + -3 = -3
-1x = -3

Divide each side by '-1'.
x = 3

Simplifying
x = 3
Solution
x = {-14, 3}