(x+9)(x+5)=77

Solution for (x+9)(x+5)=77 equation:

Simplifying
(x + 9)(x + 5) = 77

Reorder the terms:
(9 + x)(x + 5) = 77

Reorder the terms:
(9 + x)(5 + x) = 77

Multiply (9 + x) * (5 + x)
(9(5 + x) + x(5 + x)) = 77
((5 * 9 + x * 9) + x(5 + x)) = 77
((45 + 9x) + x(5 + x)) = 77
(45 + 9x + (5 * x + x * x)) = 77
(45 + 9x + (5x + x2)) = 77

Combine like terms: 9x + 5x = 14x
(45 + 14x + x2) = 77

Solving
45 + 14x + x2 = 77

Solving for variable 'x'.

Reorder the terms:
45 + -77 + 14x + x2 = 77 + -77

Combine like terms: 45 + -77 = -32
-32 + 14x + x2 = 77 + -77

Combine like terms: 77 + -77 = 0
-32 + 14x + x2 = 0

Factor a trinomial.
(-16 + -1x)(2 + -1x) = 0

Subproblem 1
Set the factor '(-16 + -1x)' equal to zero and attempt to solve:

Simplifying
-16 + -1x = 0

Solving
-16 + -1x = 0

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

Add '16' to each side of the equation.
-16 + 16 + -1x = 0 + 16

Combine like terms: -16 + 16 = 0
0 + -1x = 0 + 16
-1x = 0 + 16

Combine like terms: 0 + 16 = 16
-1x = 16

Divide each side by '-1'.
x = -16

Simplifying
x = -16
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 = {-16, 2}