(2+i)z-(3-2i)=-1+2i

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Solution for (2+i)z-(3-2i)=-1+2i equation:


Simplifying
(2 + i) * z + -1(3 + -2i) = -1 + 2i

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

Reorder the terms:
(iz + 2z) + -1(3 + -2i) = -1 + 2i
(iz + 2z) + -1(3 + -2i) = -1 + 2i
iz + 2z + (3 * -1 + -2i * -1) = -1 + 2i
iz + 2z + (-3 + 2i) = -1 + 2i

Reorder the terms:
-3 + 2i + iz + 2z = -1 + 2i

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

Reorder the terms:
-3 + 2i + -2i + iz + 2z = -1 + 2i + -2i

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

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

Solving
-3 + iz + 2z = -1

Solving for variable 'i'.

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

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

Reorder the terms:
-3 + 3 + iz + 2z = -1 + 3

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

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

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

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

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

Simplifying
i = 2z-1 + -2

Reorder the terms:
i = -2 + 2z-1

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