448=(2w+4)(w+4)

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Solution for 448=(2w+4)(w+4) equation: 


Simplifying
448 = (2w + 4)(w + 4)

Reorder the terms:
448 = (4 + 2w)(w + 4)

Reorder the terms:
448 = (4 + 2w)(4 + w)

Multiply (4 + 2w) * (4 + w)
448 = (4(4 + w) + 2w * (4 + w))
448 = ((4 * 4 + w * 4) + 2w * (4 + w))
448 = ((16 + 4w) + 2w * (4 + w))
448 = (16 + 4w + (4 * 2w + w * 2w))
448 = (16 + 4w + (8w + 2w2))

Combine like terms: 4w + 8w = 12w
448 = (16 + 12w + 2w2)

Solving
448 = 16 + 12w + 2w2

Solving for variable 'w'.

Combine like terms: 448 + -16 = 432
432 + -12w + -2w2 = 16 + 12w + 2w2 + -16 + -12w + -2w2

Reorder the terms:
432 + -12w + -2w2 = 16 + -16 + 12w + -12w + 2w2 + -2w2

Combine like terms: 16 + -16 = 0
432 + -12w + -2w2 = 0 + 12w + -12w + 2w2 + -2w2
432 + -12w + -2w2 = 12w + -12w + 2w2 + -2w2

Combine like terms: 12w + -12w = 0
432 + -12w + -2w2 = 0 + 2w2 + -2w2
432 + -12w + -2w2 = 2w2 + -2w2

Combine like terms: 2w2 + -2w2 = 0
432 + -12w + -2w2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(216 + -6w + -1w2) = 0

Factor a trinomial.
2((12 + -1w)(18 + w)) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(12 + -1w)' equal to zero and attempt to solve:

Simplifying
12 + -1w = 0

Solving
12 + -1w = 0

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

Add '-12' to each side of the equation.
12 + -12 + -1w = 0 + -12

Combine like terms: 12 + -12 = 0
0 + -1w = 0 + -12
-1w = 0 + -12

Combine like terms: 0 + -12 = -12
-1w = -12

Divide each side by '-1'.
w = 12

Simplifying
w = 12

Subproblem 2
Set the factor '(18 + w)' equal to zero and attempt to solve:

Simplifying
18 + w = 0

Solving
18 + w = 0

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

Add '-18' to each side of the equation.
18 + -18 + w = 0 + -18

Combine like terms: 18 + -18 = 0
0 + w = 0 + -18
w = 0 + -18

Combine like terms: 0 + -18 = -18
w = -18

Simplifying
w = -18
Solution
w = {12, -18}

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