396=(17+2w)(13+2w)

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Solution for 396=(17+2w)(13+2w) equation: 


Simplifying
396 = (17 + 2w)(13 + 2w)

Multiply (17 + 2w) * (13 + 2w)
396 = (17(13 + 2w) + 2w * (13 + 2w))
396 = ((13 * 17 + 2w * 17) + 2w * (13 + 2w))
396 = ((221 + 34w) + 2w * (13 + 2w))
396 = (221 + 34w + (13 * 2w + 2w * 2w))
396 = (221 + 34w + (26w + 4w2))

Combine like terms: 34w + 26w = 60w
396 = (221 + 60w + 4w2)

Solving
396 = 221 + 60w + 4w2

Solving for variable 'w'.

Combine like terms: 396 + -221 = 175
175 + -60w + -4w2 = 221 + 60w + 4w2 + -221 + -60w + -4w2

Reorder the terms:
175 + -60w + -4w2 = 221 + -221 + 60w + -60w + 4w2 + -4w2

Combine like terms: 221 + -221 = 0
175 + -60w + -4w2 = 0 + 60w + -60w + 4w2 + -4w2
175 + -60w + -4w2 = 60w + -60w + 4w2 + -4w2

Combine like terms: 60w + -60w = 0
175 + -60w + -4w2 = 0 + 4w2 + -4w2
175 + -60w + -4w2 = 4w2 + -4w2

Combine like terms: 4w2 + -4w2 = 0
175 + -60w + -4w2 = 0

Factor a trinomial.
(5 + -2w)(35 + 2w) = 0


Subproblem 1
Set the factor '(5 + -2w)' equal to zero and attempt to solve:

Simplifying
5 + -2w = 0

Solving
5 + -2w = 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 + -2w = 0 + -5

Combine like terms: 5 + -5 = 0
0 + -2w = 0 + -5
-2w = 0 + -5

Combine like terms: 0 + -5 = -5
-2w = -5

Divide each side by '-2'.
w = 2.5

Simplifying
w = 2.5

Subproblem 2
Set the factor '(35 + 2w)' equal to zero and attempt to solve:

Simplifying
35 + 2w = 0

Solving
35 + 2w = 0

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

Add '-35' to each side of the equation.
35 + -35 + 2w = 0 + -35

Combine like terms: 35 + -35 = 0
0 + 2w = 0 + -35
2w = 0 + -35

Combine like terms: 0 + -35 = -35
2w = -35

Divide each side by '2'.
w = -17.5

Simplifying
w = -17.5
Solution
w = {2.5, -17.5}

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