(x+8)(x+2)=55

Solution for (x+8)(x+2)=55 equation:

Simplifying
(x + 8)(x + 2) = 55

Reorder the terms:
(8 + x)(x + 2) = 55

Reorder the terms:
(8 + x)(2 + x) = 55

Multiply (8 + x) * (2 + x)
(8(2 + x) + x(2 + x)) = 55
((2 * 8 + x * 8) + x(2 + x)) = 55
((16 + 8x) + x(2 + x)) = 55
(16 + 8x + (2 * x + x * x)) = 55
(16 + 8x + (2x + x2)) = 55

Combine like terms: 8x + 2x = 10x
(16 + 10x + x2) = 55

Solving
16 + 10x + x2 = 55

Solving for variable 'x'.

Reorder the terms:
16 + -55 + 10x + x2 = 55 + -55

Combine like terms: 16 + -55 = -39
-39 + 10x + x2 = 55 + -55

Combine like terms: 55 + -55 = 0
-39 + 10x + x2 = 0

Factor a trinomial.
(-13 + -1x)(3 + -1x) = 0

Subproblem 1
Set the factor '(-13 + -1x)' equal to zero and attempt to solve:

Simplifying
-13 + -1x = 0

Solving
-13 + -1x = 0

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

Add '13' to each side of the equation.
-13 + 13 + -1x = 0 + 13

Combine like terms: -13 + 13 = 0
0 + -1x = 0 + 13
-1x = 0 + 13

Combine like terms: 0 + 13 = 13
-1x = 13

Divide each side by '-1'.
x = -13

Simplifying
x = -13
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 = {-13, 3}