17*(2w+4)*w=2720

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Solution for 17*(2w+4)*w=2720 equation: 


Simplifying
17(2w + 4) * w = 2720

Reorder the terms:
17(4 + 2w) * w = 2720

Reorder the terms for easier multiplication:
17w(4 + 2w) = 2720
(4 * 17w + 2w * 17w) = 2720
(68w + 34w2) = 2720

Solving
68w + 34w2 = 2720

Solving for variable 'w'.

Reorder the terms:
-2720 + 68w + 34w2 = 2720 + -2720

Combine like terms: 2720 + -2720 = 0
-2720 + 68w + 34w2 = 0

Factor out the Greatest Common Factor (GCF), '34'.
34(-80 + 2w + w2) = 0

Factor a trinomial.
34((-10 + -1w)(8 + -1w)) = 0

Ignore the factor 34.

Subproblem 1
Set the factor '(-10 + -1w)' equal to zero and attempt to solve:

Simplifying
-10 + -1w = 0

Solving
-10 + -1w = 0

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

Add '10' to each side of the equation.
-10 + 10 + -1w = 0 + 10

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

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

Divide each side by '-1'.
w = -10

Simplifying
w = -10

Subproblem 2
Set the factor '(8 + -1w)' equal to zero and attempt to solve:

Simplifying
8 + -1w = 0

Solving
8 + -1w = 0

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

Add '-8' to each side of the equation.
8 + -8 + -1w = 0 + -8

Combine like terms: 8 + -8 = 0
0 + -1w = 0 + -8
-1w = 0 + -8

Combine like terms: 0 + -8 = -8
-1w = -8

Divide each side by '-1'.
w = 8

Simplifying
w = 8
Solution
w = {-10, 8}

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