62496=(42)(2w+14)(w)

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Solution for 62496=(42)(2w+14)(w) equation: 


Simplifying
62496 = (42)(2w + 14)(w)

Reorder the terms:
62496 = 42(14 + 2w)(w)

Reorder the terms for easier multiplication:
62496 = 42w(14 + 2w)
62496 = (14 * 42w + 2w * 42w)
62496 = (588w + 84w2)

Solving
62496 = 588w + 84w2

Solving for variable 'w'.

Reorder the terms:
62496 + -588w + -84w2 = 588w + -588w + 84w2 + -84w2

Combine like terms: 588w + -588w = 0
62496 + -588w + -84w2 = 0 + 84w2 + -84w2
62496 + -588w + -84w2 = 84w2 + -84w2

Combine like terms: 84w2 + -84w2 = 0
62496 + -588w + -84w2 = 0

Factor out the Greatest Common Factor (GCF), '84'.
84(744 + -7w + -1w2) = 0

Factor a trinomial.
84((24 + -1w)(31 + w)) = 0

Ignore the factor 84.

Subproblem 1
Set the factor '(24 + -1w)' equal to zero and attempt to solve:

Simplifying
24 + -1w = 0

Solving
24 + -1w = 0

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

Add '-24' to each side of the equation.
24 + -24 + -1w = 0 + -24

Combine like terms: 24 + -24 = 0
0 + -1w = 0 + -24
-1w = 0 + -24

Combine like terms: 0 + -24 = -24
-1w = -24

Divide each side by '-1'.
w = 24

Simplifying
w = 24

Subproblem 2
Set the factor '(31 + w)' equal to zero and attempt to solve:

Simplifying
31 + w = 0

Solving
31 + w = 0

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

Add '-31' to each side of the equation.
31 + -31 + w = 0 + -31

Combine like terms: 31 + -31 = 0
0 + w = 0 + -31
w = 0 + -31

Combine like terms: 0 + -31 = -31
w = -31

Simplifying
w = -31
Solution
w = {24, -31}

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