w(j)=2(j(1-j))+j^2

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Solution for w(j)=2(j(1-j))+j^2 equation: 


Simplifying
w(j) = 2(j(1 + -1j)) + j2

Multiply w * j
jw = 2(j(1 + -1j)) + j2
jw = 2((1 * j + -1j * j)) + j2
jw = 2((1j + -1j2)) + j2
jw = (1j * 2 + -1j2 * 2) + j2
jw = (2j + -2j2) + j2

Combine like terms: -2j2 + j2 = -1j2
jw = 2j + -1j2

Solving
jw = 2j + -1j2

Solving for variable 'j'.

Reorder the terms:
-2j + jw + j2 = 2j + -1j2 + -2j + j2

Reorder the terms:
-2j + jw + j2 = 2j + -2j + -1j2 + j2

Combine like terms: 2j + -2j = 0
-2j + jw + j2 = 0 + -1j2 + j2
-2j + jw + j2 = -1j2 + j2

Combine like terms: -1j2 + j2 = 0
-2j + jw + j2 = 0

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


Subproblem 1
Set the factor 'j' equal to zero and attempt to solve:

Simplifying
j = 0

Solving
j = 0

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

Simplifying
j = 0

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

Simplifying
-2 + w + j = 0

Reorder the terms:
-2 + j + w = 0

Solving
-2 + j + w = 0

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

Add '2' to each side of the equation.
-2 + j + 2 + w = 0 + 2

Reorder the terms:
-2 + 2 + j + w = 0 + 2

Combine like terms: -2 + 2 = 0
0 + j + w = 0 + 2
j + w = 0 + 2

Combine like terms: 0 + 2 = 2
j + w = 2

Add '-1w' to each side of the equation.
j + w + -1w = 2 + -1w

Combine like terms: w + -1w = 0
j + 0 = 2 + -1w
j = 2 + -1w

Simplifying
j = 2 + -1w
Solution
j = {0, 2 + -1w}

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