3[5(4j-3)-(5-8j)]+2[2(5-j)+7]=-6

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Solution for 3[5(4j-3)-(5-8j)]+2[2(5-j)+7]=-6 equation: 


Simplifying
3[5(4j + -3) + -1(5 + -8j)] + 2[2(5 + -1j) + 7] = -6

Reorder the terms:
3[5(-3 + 4j) + -1(5 + -8j)] + 2[2(5 + -1j) + 7] = -6
3[(-3 * 5 + 4j * 5) + -1(5 + -8j)] + 2[2(5 + -1j) + 7] = -6
3[(-15 + 20j) + -1(5 + -8j)] + 2[2(5 + -1j) + 7] = -6
3[-15 + 20j + (5 * -1 + -8j * -1)] + 2[2(5 + -1j) + 7] = -6
3[-15 + 20j + (-5 + 8j)] + 2[2(5 + -1j) + 7] = -6

Reorder the terms:
3[-15 + -5 + 20j + 8j] + 2[2(5 + -1j) + 7] = -6

Combine like terms: -15 + -5 = -20
3[-20 + 20j + 8j] + 2[2(5 + -1j) + 7] = -6

Combine like terms: 20j + 8j = 28j
3[-20 + 28j] + 2[2(5 + -1j) + 7] = -6
[-20 * 3 + 28j * 3] + 2[2(5 + -1j) + 7] = -6
[-60 + 84j] + 2[2(5 + -1j) + 7] = -6
-60 + 84j + 2[(5 * 2 + -1j * 2) + 7] = -6
-60 + 84j + 2[(10 + -2j) + 7] = -6

Reorder the terms:
-60 + 84j + 2[10 + 7 + -2j] = -6

Combine like terms: 10 + 7 = 17
-60 + 84j + 2[17 + -2j] = -6
-60 + 84j + [17 * 2 + -2j * 2] = -6
-60 + 84j + [34 + -4j] = -6

Reorder the terms:
-60 + 34 + 84j + -4j = -6

Combine like terms: -60 + 34 = -26
-26 + 84j + -4j = -6

Combine like terms: 84j + -4j = 80j
-26 + 80j = -6

Solving
-26 + 80j = -6

Solving for variable 'j'.

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

Add '26' to each side of the equation.
-26 + 26 + 80j = -6 + 26

Combine like terms: -26 + 26 = 0
0 + 80j = -6 + 26
80j = -6 + 26

Combine like terms: -6 + 26 = 20
80j = 20

Divide each side by '80'.
j = 0.25

Simplifying
j = 0.25

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