i*a+b*i^2+2+3*a+3*b*i=i

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Solution for i*a+b*i^2+2+3*a+3*b*i=i equation: 


Simplifying
i * a + b * i2 + 2 + 3a + 3b * i = i

Multiply i * a
ai + b * i2 + 2 + 3a + 3b * i = i

Multiply b * i2
ai + bi2 + 2 + 3a + 3b * i = i

Multiply b * i
ai + bi2 + 2 + 3a + 3bi = i

Reorder the terms:
2 + 3a + ai + 3bi + bi2 = i

Solving
2 + 3a + ai + 3bi + bi2 = i

Solving for variable 'a'.

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

Add '-2' to each side of the equation.
2 + 3a + ai + 3bi + -2 + bi2 = -2 + i

Reorder the terms:
2 + -2 + 3a + ai + 3bi + bi2 = -2 + i

Combine like terms: 2 + -2 = 0
0 + 3a + ai + 3bi + bi2 = -2 + i
3a + ai + 3bi + bi2 = -2 + i

Add '-3bi' to each side of the equation.
3a + ai + 3bi + -3bi + bi2 = -2 + -3bi + i

Combine like terms: 3bi + -3bi = 0
3a + ai + 0 + bi2 = -2 + -3bi + i
3a + ai + bi2 = -2 + -3bi + i

Add '-1bi2' to each side of the equation.
3a + ai + bi2 + -1bi2 = -2 + -3bi + -1bi2 + i

Combine like terms: bi2 + -1bi2 = 0
3a + ai + 0 = -2 + -3bi + -1bi2 + i
3a + ai = -2 + -3bi + -1bi2 + i

Reorder the terms:
2 + 3a + ai + 3bi + bi2 + -1i = -2 + -3bi + -1bi2 + i + 2 + 3bi + bi2 + -1i

Reorder the terms:
2 + 3a + ai + 3bi + bi2 + -1i = -2 + 2 + -3bi + 3bi + -1bi2 + bi2 + i + -1i

Combine like terms: -2 + 2 = 0
2 + 3a + ai + 3bi + bi2 + -1i = 0 + -3bi + 3bi + -1bi2 + bi2 + i + -1i
2 + 3a + ai + 3bi + bi2 + -1i = -3bi + 3bi + -1bi2 + bi2 + i + -1i

Combine like terms: -3bi + 3bi = 0
2 + 3a + ai + 3bi + bi2 + -1i = 0 + -1bi2 + bi2 + i + -1i
2 + 3a + ai + 3bi + bi2 + -1i = -1bi2 + bi2 + i + -1i

Combine like terms: -1bi2 + bi2 = 0
2 + 3a + ai + 3bi + bi2 + -1i = 0 + i + -1i
2 + 3a + ai + 3bi + bi2 + -1i = i + -1i

Combine like terms: i + -1i = 0
2 + 3a + ai + 3bi + bi2 + -1i = 0

The solution to this equation could not be determined.

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