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

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


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

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

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

Solving
221 + 60w + 4w2 = 396

Solving for variable 'w'.

Reorder the terms:
221 + -396 + 60w + 4w2 = 396 + -396

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

Combine like terms: 396 + -396 = 0
-175 + 60w + 4w2 = 0

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


Subproblem 1
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

Subproblem 2
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
Solution
w = {-17.5, 2.5}

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