x^2-(4+ai)x+(b+3i)=0

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Solution for x^2-(4+ai)x+(b+3i)=0 equation:


Simplifying
x2 + -1(4 + ai) * x + (b + 3i) = 0

Reorder the terms for easier multiplication:
x2 + -1x(4 + ai) + (b + 3i) = 0
x2 + (4 * -1x + ai * -1x) + (b + 3i) = 0

Reorder the terms:
x2 + (-1aix + -4x) + (b + 3i) = 0
x2 + (-1aix + -4x) + (b + 3i) = 0

Remove parenthesis around (b + 3i)
x2 + -1aix + -4x + b + 3i = 0

Reorder the terms:
-1aix + b + 3i + -4x + x2 = 0

Solving
-1aix + b + 3i + -4x + x2 = 0

Solving for variable 'a'.

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

Add '-1b' to each side of the equation.
-1aix + b + 3i + -4x + -1b + x2 = 0 + -1b

Reorder the terms:
-1aix + b + -1b + 3i + -4x + x2 = 0 + -1b

Combine like terms: b + -1b = 0
-1aix + 0 + 3i + -4x + x2 = 0 + -1b
-1aix + 3i + -4x + x2 = 0 + -1b
Remove the zero:
-1aix + 3i + -4x + x2 = -1b

Add '-3i' to each side of the equation.
-1aix + 3i + -4x + -3i + x2 = -1b + -3i

Reorder the terms:
-1aix + 3i + -3i + -4x + x2 = -1b + -3i

Combine like terms: 3i + -3i = 0
-1aix + 0 + -4x + x2 = -1b + -3i
-1aix + -4x + x2 = -1b + -3i

Add '4x' to each side of the equation.
-1aix + -4x + 4x + x2 = -1b + -3i + 4x

Combine like terms: -4x + 4x = 0
-1aix + 0 + x2 = -1b + -3i + 4x
-1aix + x2 = -1b + -3i + 4x

Add '-1x2' to each side of the equation.
-1aix + x2 + -1x2 = -1b + -3i + 4x + -1x2

Combine like terms: x2 + -1x2 = 0
-1aix + 0 = -1b + -3i + 4x + -1x2
-1aix = -1b + -3i + 4x + -1x2

Divide each side by '-1ix'.
a = bi-1x-1 + 3x-1 + -4i-1 + i-1x

Simplifying
a = bi-1x-1 + 3x-1 + -4i-1 + i-1x

Reorder the terms:
a = bi-1x-1 + -4i-1 + i-1x + 3x-1

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