(X+2i)(6-6i)=40-10i

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Solution for (X+2i)(6-6i)=40-10i equation: 


Simplifying
(X + 2i)(6 + -6i) = 40 + -10i

Multiply (X + 2i) * (6 + -6i)
(X(6 + -6i) + 2i * (6 + -6i)) = 40 + -10i
((6 * X + -6i * X) + 2i * (6 + -6i)) = 40 + -10i
((6X + -6iX) + 2i * (6 + -6i)) = 40 + -10i
(6X + -6iX + (6 * 2i + -6i * 2i)) = 40 + -10i
(6X + -6iX + (12i + -12i2)) = 40 + -10i

Reorder the terms:
(6X + 12i + -6iX + -12i2) = 40 + -10i
(6X + 12i + -6iX + -12i2) = 40 + -10i

Solving
6X + 12i + -6iX + -12i2 = 40 + -10i

Solving for variable 'X'.

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

Add '-12i' to each side of the equation.
6X + 12i + -6iX + -12i + -12i2 = 40 + -10i + -12i

Reorder the terms:
6X + 12i + -12i + -6iX + -12i2 = 40 + -10i + -12i

Combine like terms: 12i + -12i = 0
6X + 0 + -6iX + -12i2 = 40 + -10i + -12i
6X + -6iX + -12i2 = 40 + -10i + -12i

Combine like terms: -10i + -12i = -22i
6X + -6iX + -12i2 = 40 + -22i

Add '12i2' to each side of the equation.
6X + -6iX + -12i2 + 12i2 = 40 + -22i + 12i2

Combine like terms: -12i2 + 12i2 = 0
6X + -6iX + 0 = 40 + -22i + 12i2
6X + -6iX = 40 + -22i + 12i2

Reorder the terms:
-40 + 6X + 22i + -6iX + -12i2 = 40 + -22i + 12i2 + -40 + 22i + -12i2

Reorder the terms:
-40 + 6X + 22i + -6iX + -12i2 = 40 + -40 + -22i + 22i + 12i2 + -12i2

Combine like terms: 40 + -40 = 0
-40 + 6X + 22i + -6iX + -12i2 = 0 + -22i + 22i + 12i2 + -12i2
-40 + 6X + 22i + -6iX + -12i2 = -22i + 22i + 12i2 + -12i2

Combine like terms: -22i + 22i = 0
-40 + 6X + 22i + -6iX + -12i2 = 0 + 12i2 + -12i2
-40 + 6X + 22i + -6iX + -12i2 = 12i2 + -12i2

Combine like terms: 12i2 + -12i2 = 0
-40 + 6X + 22i + -6iX + -12i2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-20 + 3X + 11i + -3iX + -6i2) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(-20 + 3X + 11i + -3iX + -6i2)' equal to zero and attempt to solve:

Simplifying
-20 + 3X + 11i + -3iX + -6i2 = 0

Solving
-20 + 3X + 11i + -3iX + -6i2 = 0

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

Add '20' to each side of the equation.
-20 + 3X + 11i + -3iX + 20 + -6i2 = 0 + 20

Reorder the terms:
-20 + 20 + 3X + 11i + -3iX + -6i2 = 0 + 20

Combine like terms: -20 + 20 = 0
0 + 3X + 11i + -3iX + -6i2 = 0 + 20
3X + 11i + -3iX + -6i2 = 0 + 20

Combine like terms: 0 + 20 = 20
3X + 11i + -3iX + -6i2 = 20

Add '-11i' to each side of the equation.
3X + 11i + -3iX + -11i + -6i2 = 20 + -11i

Reorder the terms:
3X + 11i + -11i + -3iX + -6i2 = 20 + -11i

Combine like terms: 11i + -11i = 0
3X + 0 + -3iX + -6i2 = 20 + -11i
3X + -3iX + -6i2 = 20 + -11i

Add '6i2' to each side of the equation.
3X + -3iX + -6i2 + 6i2 = 20 + -11i + 6i2

Combine like terms: -6i2 + 6i2 = 0
3X + -3iX + 0 = 20 + -11i + 6i2
3X + -3iX = 20 + -11i + 6i2

The solution to this equation could not be determined.

This subproblem is being ignored because a solution could not be determined.

The solution to this equation could not be determined.

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