(2x+17)=(x+1)(x+5)

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Solution for (2x+17)=(x+1)(x+5) equation: 


Simplifying
(2x + 17) = (x + 1)(x + 5)

Reorder the terms:
(17 + 2x) = (x + 1)(x + 5)

Remove parenthesis around (17 + 2x)
17 + 2x = (x + 1)(x + 5)

Reorder the terms:
17 + 2x = (1 + x)(x + 5)

Reorder the terms:
17 + 2x = (1 + x)(5 + x)

Multiply (1 + x) * (5 + x)
17 + 2x = (1(5 + x) + x(5 + x))
17 + 2x = ((5 * 1 + x * 1) + x(5 + x))
17 + 2x = ((5 + 1x) + x(5 + x))
17 + 2x = (5 + 1x + (5 * x + x * x))
17 + 2x = (5 + 1x + (5x + x2))

Combine like terms: 1x + 5x = 6x
17 + 2x = (5 + 6x + x2)

Solving
17 + 2x = 5 + 6x + x2

Solving for variable 'x'.

Reorder the terms:
17 + -5 + 2x + -6x + -1x2 = 5 + 6x + x2 + -5 + -6x + -1x2

Combine like terms: 17 + -5 = 12
12 + 2x + -6x + -1x2 = 5 + 6x + x2 + -5 + -6x + -1x2

Combine like terms: 2x + -6x = -4x
12 + -4x + -1x2 = 5 + 6x + x2 + -5 + -6x + -1x2

Reorder the terms:
12 + -4x + -1x2 = 5 + -5 + 6x + -6x + x2 + -1x2

Combine like terms: 5 + -5 = 0
12 + -4x + -1x2 = 0 + 6x + -6x + x2 + -1x2
12 + -4x + -1x2 = 6x + -6x + x2 + -1x2

Combine like terms: 6x + -6x = 0
12 + -4x + -1x2 = 0 + x2 + -1x2
12 + -4x + -1x2 = x2 + -1x2

Combine like terms: x2 + -1x2 = 0
12 + -4x + -1x2 = 0

Factor a trinomial.
(2 + -1x)(6 + x) = 0


Subproblem 1
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

Subproblem 2
Set the factor '(6 + x)' equal to zero and attempt to solve:

Simplifying
6 + x = 0

Solving
6 + x = 0

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

Add '-6' to each side of the equation.
6 + -6 + x = 0 + -6

Combine like terms: 6 + -6 = 0
0 + x = 0 + -6
x = 0 + -6

Combine like terms: 0 + -6 = -6
x = -6

Simplifying
x = -6
Solution
x = {2, -6}

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