(2-2j)[8+5j-(-4-2j)(-2+j)]=

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Solution for (2-2j)[8+5j-(-4-2j)(-2+j)]= equation: 


Simplifying
(2 + -2j)[8 + 5j + -1(-4 + -2j)(-2 + j)] = 0

Multiply (-4 + -2j) * (-2 + j)
(2 + -2j)[8 + 5j + -1(-4(-2 + j) + -2j * (-2 + j))] = 0
(2 + -2j)[8 + 5j + -1((-2 * -4 + j * -4) + -2j * (-2 + j))] = 0
(2 + -2j)[8 + 5j + -1((8 + -4j) + -2j * (-2 + j))] = 0
(2 + -2j)[8 + 5j + -1(8 + -4j + (-2 * -2j + j * -2j))] = 0
(2 + -2j)[8 + 5j + -1(8 + -4j + (4j + -2j2))] = 0

Combine like terms: -4j + 4j = 0
(2 + -2j)[8 + 5j + -1(8 + 0 + -2j2)] = 0
(2 + -2j)[8 + 5j + -1(8 + -2j2)] = 0
(2 + -2j)[8 + 5j + (8 * -1 + -2j2 * -1)] = 0
(2 + -2j)[8 + 5j + (-8 + 2j2)] = 0

Reorder the terms:
(2 + -2j)[8 + -8 + 5j + 2j2] = 0

Combine like terms: 8 + -8 = 0
(2 + -2j)[0 + 5j + 2j2] = 0
(2 + -2j)[5j + 2j2] = 0

Multiply (2 + -2j) * [5j + 2j2]
(2[5j + 2j2] + -2j * [5j + 2j2]) = 0
([5j * 2 + 2j2 * 2] + -2j * [5j + 2j2]) = 0
([10j + 4j2] + -2j * [5j + 2j2]) = 0
(10j + 4j2 + [5j * -2j + 2j2 * -2j]) = 0
(10j + 4j2 + [-10j2 + -4j3]) = 0

Combine like terms: 4j2 + -10j2 = -6j2
(10j + -6j2 + -4j3) = 0

Solving
10j + -6j2 + -4j3 = 0

Solving for variable 'j'.

Factor out the Greatest Common Factor (GCF), '2j'.
2j(5 + -3j + -2j2) = 0

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

Ignore the factor 2.

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

Simplifying
1 + -1j = 0

Solving
1 + -1j = 0

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

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

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

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

Divide each side by '-1'.
j = 1

Simplifying
j = 1

Subproblem 3
Set the factor '(5 + 2j)' equal to zero and attempt to solve:

Simplifying
5 + 2j = 0

Solving
5 + 2j = 0

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

Add '-5' to each side of the equation.
5 + -5 + 2j = 0 + -5

Combine like terms: 5 + -5 = 0
0 + 2j = 0 + -5
2j = 0 + -5

Combine like terms: 0 + -5 = -5
2j = -5

Divide each side by '2'.
j = -2.5

Simplifying
j = -2.5
Solution
j = {0, 1, -2.5}

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