(-4-3i)x=7+5i

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Solution for (-4-3i)x=7+5i equation:


Simplifying
(-4 + -3i) * x = 7 + 5i

Reorder the terms for easier multiplication:
x(-4 + -3i) = 7 + 5i
(-4 * x + -3i * x) = 7 + 5i

Reorder the terms:
(-3ix + -4x) = 7 + 5i
(-3ix + -4x) = 7 + 5i

Solving
-3ix + -4x = 7 + 5i

Solving for variable 'i'.

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

Add '-5i' to each side of the equation.
-3ix + -5i + -4x = 7 + 5i + -5i

Reorder the terms:
-5i + -3ix + -4x = 7 + 5i + -5i

Combine like terms: 5i + -5i = 0
-5i + -3ix + -4x = 7 + 0
-5i + -3ix + -4x = 7

Add '4x' to each side of the equation.
-5i + -3ix + -4x + 4x = 7 + 4x

Combine like terms: -4x + 4x = 0
-5i + -3ix + 0 = 7 + 4x
-5i + -3ix = 7 + 4x

Reorder the terms:
-7 + -5i + -3ix + -4x = 7 + 4x + -7 + -4x

Reorder the terms:
-7 + -5i + -3ix + -4x = 7 + -7 + 4x + -4x

Combine like terms: 7 + -7 = 0
-7 + -5i + -3ix + -4x = 0 + 4x + -4x
-7 + -5i + -3ix + -4x = 4x + -4x

Combine like terms: 4x + -4x = 0
-7 + -5i + -3ix + -4x = 0

Factor out the Greatest Common Factor (GCF), '-1'.
-1(7 + 5i + 3ix + 4x) = 0

Ignore the factor -1.

Subproblem 1

Set the factor '(7 + 5i + 3ix + 4x)' equal to zero and attempt to solve: Simplifying 7 + 5i + 3ix + 4x = 0 Solving 7 + 5i + 3ix + 4x = 0 Move all terms containing i to the left, all other terms to the right. Add '-7' to each side of the equation. 7 + 5i + 3ix + -7 + 4x = 0 + -7 Reorder the terms: 7 + -7 + 5i + 3ix + 4x = 0 + -7 Combine like terms: 7 + -7 = 0 0 + 5i + 3ix + 4x = 0 + -7 5i + 3ix + 4x = 0 + -7 Combine like terms: 0 + -7 = -7 5i + 3ix + 4x = -7 Add '-4x' to each side of the equation. 5i + 3ix + 4x + -4x = -7 + -4x Combine like terms: 4x + -4x = 0 5i + 3ix + 0 = -7 + -4x 5i + 3ix = -7 + -4x 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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