220=2w+2w(2w-40)

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Solution for 220=2w+2w(2w-40) equation:


Simplifying
220 = 2w + 2w(2w + -40)

Reorder the terms:
220 = 2w + 2w(-40 + 2w)
220 = 2w + (-40 * 2w + 2w * 2w)
220 = 2w + (-80w + 4w2)

Combine like terms: 2w + -80w = -78w
220 = -78w + 4w2

Solving
220 = -78w + 4w2

Solving for variable 'w'.

Reorder the terms:
220 + 78w + -4w2 = -78w + 78w + 4w2 + -4w2

Combine like terms: -78w + 78w = 0
220 + 78w + -4w2 = 0 + 4w2 + -4w2
220 + 78w + -4w2 = 4w2 + -4w2

Combine like terms: 4w2 + -4w2 = 0
220 + 78w + -4w2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(110 + 39w + -2w2) = 0

Factor a trinomial.
2((22 + -1w)(5 + 2w)) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(22 + -1w)' equal to zero and attempt to solve:

Simplifying
22 + -1w = 0

Solving
22 + -1w = 0

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

Add '-22' to each side of the equation.
22 + -22 + -1w = 0 + -22

Combine like terms: 22 + -22 = 0
0 + -1w = 0 + -22
-1w = 0 + -22

Combine like terms: 0 + -22 = -22
-1w = -22

Divide each side by '-1'.
w = 22

Simplifying
w = 22

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 = {22, -2.5}

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