(2x+4)+(4y-6)i=8-10i

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Solution for (2x+4)+(4y-6)i=8-10i equation:


Simplifying
(2x + 4) + (4y + -6) * i = 8 + -10i

Reorder the terms:
(4 + 2x) + (4y + -6) * i = 8 + -10i

Remove parenthesis around (4 + 2x)
4 + 2x + (4y + -6) * i = 8 + -10i

Reorder the terms:
4 + 2x + (-6 + 4y) * i = 8 + -10i

Reorder the terms for easier multiplication:
4 + 2x + i(-6 + 4y) = 8 + -10i
4 + 2x + (-6 * i + 4y * i) = 8 + -10i
4 + 2x + (-6i + 4iy) = 8 + -10i

Reorder the terms:
4 + -6i + 4iy + 2x = 8 + -10i

Solving
4 + -6i + 4iy + 2x = 8 + -10i

Solving for variable 'i'.

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

Add '10i' to each side of the equation.
4 + -6i + 4iy + 10i + 2x = 8 + -10i + 10i

Reorder the terms:
4 + -6i + 10i + 4iy + 2x = 8 + -10i + 10i

Combine like terms: -6i + 10i = 4i
4 + 4i + 4iy + 2x = 8 + -10i + 10i

Combine like terms: -10i + 10i = 0
4 + 4i + 4iy + 2x = 8 + 0
4 + 4i + 4iy + 2x = 8

Add '-4' to each side of the equation.
4 + 4i + 4iy + -4 + 2x = 8 + -4

Reorder the terms:
4 + -4 + 4i + 4iy + 2x = 8 + -4

Combine like terms: 4 + -4 = 0
0 + 4i + 4iy + 2x = 8 + -4
4i + 4iy + 2x = 8 + -4

Combine like terms: 8 + -4 = 4
4i + 4iy + 2x = 4

Add '-2x' to each side of the equation.
4i + 4iy + 2x + -2x = 4 + -2x

Combine like terms: 2x + -2x = 0
4i + 4iy + 0 = 4 + -2x
4i + 4iy = 4 + -2x

Reorder the terms:
-4 + 4i + 4iy + 2x = 4 + -2x + -4 + 2x

Reorder the terms:
-4 + 4i + 4iy + 2x = 4 + -4 + -2x + 2x

Combine like terms: 4 + -4 = 0
-4 + 4i + 4iy + 2x = 0 + -2x + 2x
-4 + 4i + 4iy + 2x = -2x + 2x

Combine like terms: -2x + 2x = 0
-4 + 4i + 4iy + 2x = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-2 + 2i + 2iy + x) = 0

Ignore the factor 2.

Subproblem 1

Set the factor '(-2 + 2i + 2iy + x)' equal to zero and attempt to solve: Simplifying -2 + 2i + 2iy + x = 0 Solving -2 + 2i + 2iy + x = 0 Move all terms containing i to the left, all other terms to the right. Add '2' to each side of the equation. -2 + 2i + 2iy + 2 + x = 0 + 2 Reorder the terms: -2 + 2 + 2i + 2iy + x = 0 + 2 Combine like terms: -2 + 2 = 0 0 + 2i + 2iy + x = 0 + 2 2i + 2iy + x = 0 + 2 Combine like terms: 0 + 2 = 2 2i + 2iy + x = 2 Add '-1x' to each side of the equation. 2i + 2iy + x + -1x = 2 + -1x Combine like terms: x + -1x = 0 2i + 2iy + 0 = 2 + -1x 2i + 2iy = 2 + -1x 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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