f(x)=a[x-2][x-(-3-2i)][x-(-3+2i)]

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Solution for f(x)=a[x-2][x-(-3-2i)][x-(-3+2i)] equation:


Simplifying
f(x) = a[x + -2][x + -1(-3 + -2i)][x + -1(-3 + 2i)]

Multiply f * x
fx = a[x + -2][x + -1(-3 + -2i)][x + -1(-3 + 2i)]

Reorder the terms:
fx = a[-2 + x][x + -1(-3 + -2i)][x + -1(-3 + 2i)]
fx = a[-2 + x][x + (-3 * -1 + -2i * -1)][x + -1(-3 + 2i)]
fx = a[-2 + x][x + (3 + 2i)][x + -1(-3 + 2i)]

Reorder the terms:
fx = a[-2 + x][3 + 2i + x][x + -1(-3 + 2i)]
fx = a[-2 + x][3 + 2i + x][x + (-3 * -1 + 2i * -1)]
fx = a[-2 + x][3 + 2i + x][x + (3 + -2i)]

Reorder the terms:
fx = a[-2 + x][3 + 2i + x][3 + -2i + x]

Multiply [-2 + x] * [3 + 2i + x]
fx = a[-2[3 + 2i + x] + x[3 + 2i + x]][3 + -2i + x]
fx = a[[3 * -2 + 2i * -2 + x * -2] + x[3 + 2i + x]][3 + -2i + x]
fx = a[[-6 + -4i + -2x] + x[3 + 2i + x]][3 + -2i + x]
fx = a[-6 + -4i + -2x + [3 * x + 2i * x + x * x]][3 + -2i + x]

Reorder the terms:
fx = a[-6 + -4i + -2x + [2ix + 3x + x2]][3 + -2i + x]
fx = a[-6 + -4i + -2x + [2ix + 3x + x2]][3 + -2i + x]

Reorder the terms:
fx = a[-6 + -4i + 2ix + -2x + 3x + x2][3 + -2i + x]

Combine like terms: -2x + 3x = 1x
fx = a[-6 + -4i + 2ix + 1x + x2][3 + -2i + x]

Multiply [-6 + -4i + 2ix + 1x + x2] * [3 + -2i + x]
fx = a[-6[3 + -2i + x] + -4i * [3 + -2i + x] + 2ix * [3 + -2i + x] + 1x * [3 + -2i + x] + x2[3 + -2i + x]]
fx = a[[3 * -6 + -2i * -6 + x * -6] + -4i * [3 + -2i + x] + 2ix * [3 + -2i + x] + 1x * [3 + -2i + x] + x2[3 + -2i + x]]
fx = a[[-18 + 12i + -6x] + -4i * [3 + -2i + x] + 2ix * [3 + -2i + x] + 1x * [3 + -2i + x] + x2[3 + -2i + x]]
fx = a[-18 + 12i + -6x + [3 * -4i + -2i * -4i + x * -4i] + 2ix * [3 + -2i + x] + 1x * [3 + -2i + x] + x2[3 + -2i + x]]

Reorder the terms:
fx = a[-18 + 12i + -6x + [-12i + -4ix + 8i2] + 2ix * [3 + -2i + x] + 1x * [3 + -2i + x] + x2[3 + -2i + x]]
fx = a[-18 + 12i + -6x + [-12i + -4ix + 8i2] + 2ix * [3 + -2i + x] + 1x * [3 + -2i + x] + x2[3 + -2i + x]]
fx = a[-18 + 12i + -6x + -12i + -4ix + 8i2 + [3 * 2ix + -2i * 2ix + x * 2ix] + 1x * [3 + -2i + x] + x2[3 + -2i + x]]

Reorder the terms:
fx = a[-18 + 12i + -6x + -12i + -4ix + 8i2 + [6ix + 2ix2 + -4i2x] + 1x * [3 + -2i + x] + x2[3 + -2i + x]]
fx = a[-18 + 12i + -6x + -12i + -4ix + 8i2 + [6ix + 2ix2 + -4i2x] + 1x * [3 + -2i + x] + x2[3 + -2i + x]]
fx = a[-18 + 12i + -6x + -12i + -4ix + 8i2 + 6ix + 2ix2 + -4i2x + [3 * 1x + -2i * 1x + x * 1x] + x2[3 + -2i + x]]

Reorder the terms:
fx = a[-18 + 12i + -6x + -12i + -4ix + 8i2 + 6ix + 2ix2 + -4i2x + [-2ix + 3x + 1x2] + x2[3 + -2i + x]]
fx = a[-18 + 12i + -6x + -12i + -4ix + 8i2 + 6ix + 2ix2 + -4i2x + [-2ix + 3x + 1x2] + x2[3 + -2i + x]]
fx = a[-18 + 12i + -6x + -12i + -4ix + 8i2 + 6ix + 2ix2 + -4i2x + -2ix + 3x + 1x2 + [3 * x2 + -2i * x2 + x * x2]]

Reorder the terms:
fx = a[-18 + 12i + -6x + -12i + -4ix + 8i2 + 6ix + 2ix2 + -4i2x + -2ix + 3x + 1x2 + [-2ix2 + 3x2 + x3]]
fx = a[-18 + 12i + -6x + -12i + -4ix + 8i2 + 6ix + 2ix2 + -4i2x + -2ix + 3x + 1x2 + [-2ix2 + 3x2 + x3]]

Reorder the terms:
fx = a[-18 + 12i + -12i + -4ix + 6ix + -2ix + 2ix2 + -2ix2 + 8i2 + -4i2x + -6x + 3x + 1x2 + 3x2 + x3]

Combine like terms: 12i + -12i = 0
fx = a[-18 + 0 + -4ix + 6ix + -2ix + 2ix2 + -2ix2 + 8i2 + -4i2x + -6x + 3x + 1x2 + 3x2 + x3]
fx = a[-18 + -4ix + 6ix + -2ix + 2ix2 + -2ix2 + 8i2 + -4i2x + -6x + 3x + 1x2 + 3x2 + x3]

Combine like terms: -4ix + 6ix = 2ix
fx = a[-18 + 2ix + -2ix + 2ix2 + -2ix2 + 8i2 + -4i2x + -6x + 3x + 1x2 + 3x2 + x3]

Combine like terms: 2ix + -2ix = 0
fx = a[-18 + 0 + 2ix2 + -2ix2 + 8i2 + -4i2x + -6x + 3x + 1x2 + 3x2 + x3]
fx = a[-18 + 2ix2 + -2ix2 + 8i2 + -4i2x + -6x + 3x + 1x2 + 3x2 + x3]

Combine like terms: 2ix2 + -2ix2 = 0
fx = a[-18 + 0 + 8i2 + -4i2x + -6x + 3x + 1x2 + 3x2 + x3]
fx = a[-18 + 8i2 + -4i2x + -6x + 3x + 1x2 + 3x2 + x3]

Combine like terms: -6x + 3x = -3x
fx = a[-18 + 8i2 + -4i2x + -3x + 1x2 + 3x2 + x3]

Combine like terms: 1x2 + 3x2 = 4x2
fx = a[-18 + 8i2 + -4i2x + -3x + 4x2 + x3]
fx = [-18 * a + 8i2 * a + -4i2x * a + -3x * a + 4x2 * a + x3 * a]
fx = [-18a + 8ai2 + -4ai2x + -3ax + 4ax2 + ax3]

Solving
fx = -18a + 8ai2 + -4ai2x + -3ax + 4ax2 + ax3

Solving for variable 'f'.

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

Divide each side by 'x'.
f = -18ax-1 + 8ai2x-1 + -4ai2 + -3a + 4ax + ax2

Simplifying
f = -18ax-1 + 8ai2x-1 + -4ai2 + -3a + 4ax + ax2

Reorder the terms:
f = -3a + -4ai2 + 8ai2x-1 + -18ax-1 + 4ax + ax2

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