2x+3i(2x+3)=(1+i)x+9i

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Solution for 2x+3i(2x+3)=(1+i)x+9i equation: 


Simplifying
2x + 3i(2x + 3) = (1 + i) * x + 9i

Reorder the terms:
2x + 3i(3 + 2x) = (1 + i) * x + 9i
2x + (3 * 3i + 2x * 3i) = (1 + i) * x + 9i
2x + (9i + 6ix) = (1 + i) * x + 9i

Reorder the terms:
9i + 6ix + 2x = (1 + i) * x + 9i

Reorder the terms for easier multiplication:
9i + 6ix + 2x = x(1 + i) + 9i
9i + 6ix + 2x = (1 * x + i * x) + 9i

Reorder the terms:
9i + 6ix + 2x = (ix + 1x) + 9i
9i + 6ix + 2x = (ix + 1x) + 9i

Reorder the terms:
9i + 6ix + 2x = 9i + ix + 1x

Add '-9i' to each side of the equation.
9i + 6ix + -9i + 2x = 9i + ix + -9i + 1x

Reorder the terms:
9i + -9i + 6ix + 2x = 9i + ix + -9i + 1x

Combine like terms: 9i + -9i = 0
0 + 6ix + 2x = 9i + ix + -9i + 1x
6ix + 2x = 9i + ix + -9i + 1x

Reorder the terms:
6ix + 2x = 9i + -9i + ix + 1x

Combine like terms: 9i + -9i = 0
6ix + 2x = 0 + ix + 1x
6ix + 2x = ix + 1x

Solving
6ix + 2x = ix + 1x

Solving for variable 'i'.

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

Add '-1ix' to each side of the equation.
6ix + -1ix + 2x = ix + -1ix + 1x

Combine like terms: 6ix + -1ix = 5ix
5ix + 2x = ix + -1ix + 1x

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

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

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

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

Divide each side by '5x'.
i = -0.2

Simplifying
i = -0.2

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