x+(2x+5)i=x-(5+3x)i

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Solution for x+(2x+5)i=x-(5+3x)i equation: 


Simplifying
x + (2x + 5) * i = x + -1(5 + 3x) * i

Reorder the terms:
x + (5 + 2x) * i = x + -1(5 + 3x) * i

Reorder the terms for easier multiplication:
x + i(5 + 2x) = x + -1(5 + 3x) * i
x + (5 * i + 2x * i) = x + -1(5 + 3x) * i
x + (5i + 2ix) = x + -1(5 + 3x) * i

Reorder the terms:
5i + 2ix + x = x + -1(5 + 3x) * i

Reorder the terms for easier multiplication:
5i + 2ix + x = x + -1i(5 + 3x)
5i + 2ix + x = x + (5 * -1i + 3x * -1i)
5i + 2ix + x = x + (-5i + -3ix)

Reorder the terms:
5i + 2ix + x = -5i + -3ix + x

Add '-1x' to each side of the equation.
5i + 2ix + x + -1x = -5i + -3ix + x + -1x

Combine like terms: x + -1x = 0
5i + 2ix + 0 = -5i + -3ix + x + -1x
5i + 2ix = -5i + -3ix + x + -1x

Combine like terms: x + -1x = 0
5i + 2ix = -5i + -3ix + 0
5i + 2ix = -5i + -3ix

Solving
5i + 2ix = -5i + -3ix

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.
5i + 5i + 2ix = -5i + 5i + -3ix

Combine like terms: 5i + 5i = 10i
10i + 2ix = -5i + 5i + -3ix

Combine like terms: -5i + 5i = 0
10i + 2ix = 0 + -3ix
10i + 2ix = -3ix

Add '3ix' to each side of the equation.
10i + 2ix + 3ix = -3ix + 3ix

Combine like terms: 2ix + 3ix = 5ix
10i + 5ix = -3ix + 3ix

Combine like terms: -3ix + 3ix = 0
10i + 5ix = 0

Factor out the Greatest Common Factor (GCF), '5i'.
5i(2 + x) = 0

Ignore the factor 5.

Subproblem 1
Set the factor 'i' equal to zero and attempt to solve:

Simplifying
i = 0

Solving
i = 0

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

Simplifying
i = 0

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

Simplifying
2 + x = 0

Solving
2 + 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 + -2 + x = 0 + -2

Combine like terms: 2 + -2 = 0
0 + x = 0 + -2
x = 0 + -2

Combine like terms: 0 + -2 = -2
x = -2

Add '-1x' to each side of the equation.
x + -1x = -2 + -1x

Combine like terms: x + -1x = 0
0 = -2 + -1x

Simplifying
0 = -2 + -1x

The solution to this equation could not be determined.

This subproblem is being ignored because a solution could not be determined.
Solution
i = {0}

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