5w+17=(w+1)(w+7)

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Solution for 5w+17=(w+1)(w+7) equation: 


Simplifying
5w + 17 = (w + 1)(w + 7)

Reorder the terms:
17 + 5w = (w + 1)(w + 7)

Reorder the terms:
17 + 5w = (1 + w)(w + 7)

Reorder the terms:
17 + 5w = (1 + w)(7 + w)

Multiply (1 + w) * (7 + w)
17 + 5w = (1(7 + w) + w(7 + w))
17 + 5w = ((7 * 1 + w * 1) + w(7 + w))
17 + 5w = ((7 + 1w) + w(7 + w))
17 + 5w = (7 + 1w + (7 * w + w * w))
17 + 5w = (7 + 1w + (7w + w2))

Combine like terms: 1w + 7w = 8w
17 + 5w = (7 + 8w + w2)

Solving
17 + 5w = 7 + 8w + w2

Solving for variable 'w'.

Reorder the terms:
17 + -7 + 5w + -8w + -1w2 = 7 + 8w + w2 + -7 + -8w + -1w2

Combine like terms: 17 + -7 = 10
10 + 5w + -8w + -1w2 = 7 + 8w + w2 + -7 + -8w + -1w2

Combine like terms: 5w + -8w = -3w
10 + -3w + -1w2 = 7 + 8w + w2 + -7 + -8w + -1w2

Reorder the terms:
10 + -3w + -1w2 = 7 + -7 + 8w + -8w + w2 + -1w2

Combine like terms: 7 + -7 = 0
10 + -3w + -1w2 = 0 + 8w + -8w + w2 + -1w2
10 + -3w + -1w2 = 8w + -8w + w2 + -1w2

Combine like terms: 8w + -8w = 0
10 + -3w + -1w2 = 0 + w2 + -1w2
10 + -3w + -1w2 = w2 + -1w2

Combine like terms: w2 + -1w2 = 0
10 + -3w + -1w2 = 0

Factor a trinomial.
(2 + -1w)(5 + w) = 0


Subproblem 1
Set the factor '(2 + -1w)' equal to zero and attempt to solve:

Simplifying
2 + -1w = 0

Solving
2 + -1w = 0

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

Add '-2' to each side of the equation.
2 + -2 + -1w = 0 + -2

Combine like terms: 2 + -2 = 0
0 + -1w = 0 + -2
-1w = 0 + -2

Combine like terms: 0 + -2 = -2
-1w = -2

Divide each side by '-1'.
w = 2

Simplifying
w = 2

Subproblem 2
Set the factor '(5 + w)' equal to zero and attempt to solve:

Simplifying
5 + w = 0

Solving
5 + w = 0

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

Add '-5' to each side of the equation.
5 + -5 + w = 0 + -5

Combine like terms: 5 + -5 = 0
0 + w = 0 + -5
w = 0 + -5

Combine like terms: 0 + -5 = -5
w = -5

Simplifying
w = -5
Solution
w = {2, -5}

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