z^2+(2i-3)*z+5-7=0

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Solution for z^2+(2i-3)*z+5-7=0 equation:


Simplifying
z2 + (2i + -3) * z + 5 + -7 = 0

Reorder the terms:
z2 + (-3 + 2i) * z + 5 + -7 = 0

Reorder the terms for easier multiplication:
z2 + z(-3 + 2i) + 5 + -7 = 0
z2 + (-3 * z + 2i * z) + 5 + -7 = 0

Reorder the terms:
z2 + (2iz + -3z) + 5 + -7 = 0
z2 + (2iz + -3z) + 5 + -7 = 0

Reorder the terms:
5 + -7 + 2iz + -3z + z2 = 0

Combine like terms: 5 + -7 = -2
-2 + 2iz + -3z + z2 = 0

Solving
-2 + 2iz + -3z + z2 = 0

Solving for variable 'i'.

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

Add '2' to each side of the equation.
-2 + 2iz + -3z + 2 + z2 = 0 + 2

Reorder the terms:
-2 + 2 + 2iz + -3z + z2 = 0 + 2

Combine like terms: -2 + 2 = 0
0 + 2iz + -3z + z2 = 0 + 2
2iz + -3z + z2 = 0 + 2

Combine like terms: 0 + 2 = 2
2iz + -3z + z2 = 2

Add '3z' to each side of the equation.
2iz + -3z + 3z + z2 = 2 + 3z

Combine like terms: -3z + 3z = 0
2iz + 0 + z2 = 2 + 3z
2iz + z2 = 2 + 3z

Add '-1z2' to each side of the equation.
2iz + z2 + -1z2 = 2 + 3z + -1z2

Combine like terms: z2 + -1z2 = 0
2iz + 0 = 2 + 3z + -1z2
2iz = 2 + 3z + -1z2

Divide each side by '2z'.
i = z-1 + 1.5 + -0.5z

Simplifying
i = z-1 + 1.5 + -0.5z

Reorder the terms:
i = 1.5 + z-1 + -0.5z

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