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

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


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

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

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

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

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

Solving
55 = 16 + 10x + x2

Solving for variable 'x'.

Combine like terms: 55 + -16 = 39
39 + -10x + -1x2 = 16 + 10x + x2 + -16 + -10x + -1x2

Reorder the terms:
39 + -10x + -1x2 = 16 + -16 + 10x + -10x + x2 + -1x2

Combine like terms: 16 + -16 = 0
39 + -10x + -1x2 = 0 + 10x + -10x + x2 + -1x2
39 + -10x + -1x2 = 10x + -10x + x2 + -1x2

Combine like terms: 10x + -10x = 0
39 + -10x + -1x2 = 0 + x2 + -1x2
39 + -10x + -1x2 = x2 + -1x2

Combine like terms: x2 + -1x2 = 0
39 + -10x + -1x2 = 0

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


Subproblem 1
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

Subproblem 2
Set the factor '(13 + x)' equal to zero and attempt to solve:

Simplifying
13 + x = 0

Solving
13 + x = 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 + x = 0 + -13

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

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

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

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