w(2w-2)=220

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


Simplifying
w(2w + -2) = 220

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

Solving
-2w + 2w2 = 220

Solving for variable 'w'.

Reorder the terms:
-220 + -2w + 2w2 = 220 + -220

Combine like terms: 220 + -220 = 0
-220 + -2w + 2w2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-110 + -1w + w2) = 0

Factor a trinomial.
2((-10 + -1w)(11 + -1w)) = 0

Ignore the factor 2.

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 '(11 + -1w)' equal to zero and attempt to solve:

Simplifying
11 + -1w = 0

Solving
11 + -1w = 0

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

Add '-11' to each side of the equation.
11 + -11 + -1w = 0 + -11

Combine like terms: 11 + -11 = 0
0 + -1w = 0 + -11
-1w = 0 + -11

Combine like terms: 0 + -11 = -11
-1w = -11

Divide each side by '-1'.
w = 11

Simplifying
w = 11
Solution
w = {-10, 11}

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