F(x)=an(x+4)(X-3-5i)(x-3+5i)

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Solution for F(x)=an(x+4)(X-3-5i)(x-3+5i) equation: 


Simplifying
F(x) = an(x + 4)(X + -3 + -5i)(x + -3 + 5i)

Multiply F * x
xF = an(x + 4)(X + -3 + -5i)(x + -3 + 5i)

Reorder the terms:
xF = an(4 + x)(X + -3 + -5i)(x + -3 + 5i)

Reorder the terms:
xF = an(4 + x)(-3 + X + -5i)(x + -3 + 5i)

Reorder the terms:
xF = an(4 + x)(-3 + X + -5i)(-3 + 5i + x)

Multiply (4 + x) * (-3 + X + -5i)
xF = an(4(-3 + X + -5i) + x(-3 + X + -5i))(-3 + 5i + x)
xF = an((-3 * 4 + X * 4 + -5i * 4) + x(-3 + X + -5i))(-3 + 5i + x)
xF = an((-12 + 4X + -20i) + x(-3 + X + -5i))(-3 + 5i + x)
xF = an(-12 + 4X + -20i + (-3 * x + X * x + -5i * x))(-3 + 5i + x)

Reorder the terms:
xF = an(-12 + 4X + -20i + (-5ix + -3x + xX))(-3 + 5i + x)
xF = an(-12 + 4X + -20i + (-5ix + -3x + xX))(-3 + 5i + x)
xF = an(-12 + 4X + -20i + -5ix + -3x + xX)(-3 + 5i + x)

Multiply (-12 + 4X + -20i + -5ix + -3x + xX) * (-3 + 5i + x)
xF = an(-12(-3 + 5i + x) + 4X * (-3 + 5i + x) + -20i * (-3 + 5i + x) + -5ix * (-3 + 5i + x) + -3x * (-3 + 5i + x) + xX(-3 + 5i + x))
xF = an((-3 * -12 + 5i * -12 + x * -12) + 4X * (-3 + 5i + x) + -20i * (-3 + 5i + x) + -5ix * (-3 + 5i + x) + -3x * (-3 + 5i + x) + xX(-3 + 5i + x))
xF = an((36 + -60i + -12x) + 4X * (-3 + 5i + x) + -20i * (-3 + 5i + x) + -5ix * (-3 + 5i + x) + -3x * (-3 + 5i + x) + xX(-3 + 5i + x))
xF = an(36 + -60i + -12x + (-3 * 4X + 5i * 4X + x * 4X) + -20i * (-3 + 5i + x) + -5ix * (-3 + 5i + x) + -3x * (-3 + 5i + x) + xX(-3 + 5i + x))
xF = an(36 + -60i + -12x + (-12X + 20iX + 4xX) + -20i * (-3 + 5i + x) + -5ix * (-3 + 5i + x) + -3x * (-3 + 5i + x) + xX(-3 + 5i + x))
xF = an(36 + -60i + -12x + -12X + 20iX + 4xX + (-3 * -20i + 5i * -20i + x * -20i) + -5ix * (-3 + 5i + x) + -3x * (-3 + 5i + x) + xX(-3 + 5i + x))

Reorder the terms:
xF = an(36 + -60i + -12x + -12X + 20iX + 4xX + (60i + -20ix + -100i2) + -5ix * (-3 + 5i + x) + -3x * (-3 + 5i + x) + xX(-3 + 5i + x))
xF = an(36 + -60i + -12x + -12X + 20iX + 4xX + (60i + -20ix + -100i2) + -5ix * (-3 + 5i + x) + -3x * (-3 + 5i + x) + xX(-3 + 5i + x))
xF = an(36 + -60i + -12x + -12X + 20iX + 4xX + 60i + -20ix + -100i2 + (-3 * -5ix + 5i * -5ix + x * -5ix) + -3x * (-3 + 5i + x) + xX(-3 + 5i + x))

Reorder the terms:
xF = an(36 + -60i + -12x + -12X + 20iX + 4xX + 60i + -20ix + -100i2 + (15ix + -5ix2 + -25i2x) + -3x * (-3 + 5i + x) + xX(-3 + 5i + x))
xF = an(36 + -60i + -12x + -12X + 20iX + 4xX + 60i + -20ix + -100i2 + (15ix + -5ix2 + -25i2x) + -3x * (-3 + 5i + x) + xX(-3 + 5i + x))
xF = an(36 + -60i + -12x + -12X + 20iX + 4xX + 60i + -20ix + -100i2 + 15ix + -5ix2 + -25i2x + (-3 * -3x + 5i * -3x + x * -3x) + xX(-3 + 5i + x))

Reorder the terms:
xF = an(36 + -60i + -12x + -12X + 20iX + 4xX + 60i + -20ix + -100i2 + 15ix + -5ix2 + -25i2x + (-15ix + 9x + -3x2) + xX(-3 + 5i + x))
xF = an(36 + -60i + -12x + -12X + 20iX + 4xX + 60i + -20ix + -100i2 + 15ix + -5ix2 + -25i2x + (-15ix + 9x + -3x2) + xX(-3 + 5i + x))
xF = an(36 + -60i + -12x + -12X + 20iX + 4xX + 60i + -20ix + -100i2 + 15ix + -5ix2 + -25i2x + -15ix + 9x + -3x2 + (-3 * xX + 5i * xX + x * xX))

Reorder the terms:
xF = an(36 + -60i + -12x + -12X + 20iX + 4xX + 60i + -20ix + -100i2 + 15ix + -5ix2 + -25i2x + -15ix + 9x + -3x2 + (5ixX + -3xX + x2X))
xF = an(36 + -60i + -12x + -12X + 20iX + 4xX + 60i + -20ix + -100i2 + 15ix + -5ix2 + -25i2x + -15ix + 9x + -3x2 + (5ixX + -3xX + x2X))

Reorder the terms:
xF = an(36 + -12X + -60i + 60i + 20iX + -20ix + 15ix + -15ix + 5ixX + -5ix2 + -100i2 + -25i2x + -12x + 9x + 4xX + -3xX + -3x2 + x2X)

Combine like terms: -60i + 60i = 0
xF = an(36 + -12X + 0 + 20iX + -20ix + 15ix + -15ix + 5ixX + -5ix2 + -100i2 + -25i2x + -12x + 9x + 4xX + -3xX + -3x2 + x2X)
xF = an(36 + -12X + 20iX + -20ix + 15ix + -15ix + 5ixX + -5ix2 + -100i2 + -25i2x + -12x + 9x + 4xX + -3xX + -3x2 + x2X)

Combine like terms: -20ix + 15ix = -5ix
xF = an(36 + -12X + 20iX + -5ix + -15ix + 5ixX + -5ix2 + -100i2 + -25i2x + -12x + 9x + 4xX + -3xX + -3x2 + x2X)

Combine like terms: -5ix + -15ix = -20ix
xF = an(36 + -12X + 20iX + -20ix + 5ixX + -5ix2 + -100i2 + -25i2x + -12x + 9x + 4xX + -3xX + -3x2 + x2X)

Combine like terms: -12x + 9x = -3x
xF = an(36 + -12X + 20iX + -20ix + 5ixX + -5ix2 + -100i2 + -25i2x + -3x + 4xX + -3xX + -3x2 + x2X)

Combine like terms: 4xX + -3xX = 1xX
xF = an(36 + -12X + 20iX + -20ix + 5ixX + -5ix2 + -100i2 + -25i2x + -3x + 1xX + -3x2 + x2X)
xF = (36 * an + -12X * an + 20iX * an + -20ix * an + 5ixX * an + -5ix2 * an + -100i2 * an + -25i2x * an + -3x * an + 1xX * an + -3x2 * an + x2X * an)

Reorder the terms:
xF = (20ainX + -20ainx + 5ainxX + -5ainx2 + -100ai2n + -25ai2nx + 36an + -12anX + -3anx + 1anxX + -3anx2 + anx2X)
xF = (20ainX + -20ainx + 5ainxX + -5ainx2 + -100ai2n + -25ai2nx + 36an + -12anX + -3anx + 1anxX + -3anx2 + anx2X)

Solving
xF = 20ainX + -20ainx + 5ainxX + -5ainx2 + -100ai2n + -25ai2nx + 36an + -12anX + -3anx + 1anxX + -3anx2 + anx2X

Solving for variable 'x'.

Reorder the terms:
-20ainX + 20ainx + -5ainxX + 5ainx2 + 100ai2n + 25ai2nx + -36an + 12anX + 3anx + -1anxX + 3anx2 + -1anx2X + xF = 20ainX + -20ainx + 5ainxX + -5ainx2 + -100ai2n + -25ai2nx + 36an + -12anX + -3anx + 1anxX + -3anx2 + anx2X + -20ainX + 20ainx + -5ainxX + 5ainx2 + 100ai2n + 25ai2nx + -36an + 12anX + 3anx + -1anxX + 3anx2 + -1anx2X

Reorder the terms:
-20ainX + 20ainx + -5ainxX + 5ainx2 + 100ai2n + 25ai2nx + -36an + 12anX + 3anx + -1anxX + 3anx2 + -1anx2X + xF = 20ainX + -20ainX + -20ainx + 20ainx + 5ainxX + -5ainxX + -5ainx2 + 5ainx2 + -100ai2n + 100ai2n + -25ai2nx + 25ai2nx + 36an + -36an + -12anX + 12anX + -3anx + 3anx + 1anxX + -1anxX + -3anx2 + 3anx2 + anx2X + -1anx2X

Combine like terms: 20ainX + -20ainX = 0
-20ainX + 20ainx + -5ainxX + 5ainx2 + 100ai2n + 25ai2nx + -36an + 12anX + 3anx + -1anxX + 3anx2 + -1anx2X + xF = 0 + -20ainx + 20ainx + 5ainxX + -5ainxX + -5ainx2 + 5ainx2 + -100ai2n + 100ai2n + -25ai2nx + 25ai2nx + 36an + -36an + -12anX + 12anX + -3anx + 3anx + 1anxX + -1anxX + -3anx2 + 3anx2 + anx2X + -1anx2X
-20ainX + 20ainx + -5ainxX + 5ainx2 + 100ai2n + 25ai2nx + -36an + 12anX + 3anx + -1anxX + 3anx2 + -1anx2X + xF = -20ainx + 20ainx + 5ainxX + -5ainxX + -5ainx2 + 5ainx2 + -100ai2n + 100ai2n + -25ai2nx + 25ai2nx + 36an + -36an + -12anX + 12anX + -3anx + 3anx + 1anxX + -1anxX + -3anx2 + 3anx2 + anx2X + -1anx2X

Combine like terms: -20ainx + 20ainx = 0
-20ainX + 20ainx + -5ainxX + 5ainx2 + 100ai2n + 25ai2nx + -36an + 12anX + 3anx + -1anxX + 3anx2 + -1anx2X + xF = 0 + 5ainxX + -5ainxX + -5ainx2 + 5ainx2 + -100ai2n + 100ai2n + -25ai2nx + 25ai2nx + 36an + -36an + -12anX + 12anX + -3anx + 3anx + 1anxX + -1anxX + -3anx2 + 3anx2 + anx2X + -1anx2X
-20ainX + 20ainx + -5ainxX + 5ainx2 + 100ai2n + 25ai2nx + -36an + 12anX + 3anx + -1anxX + 3anx2 + -1anx2X + xF = 5ainxX + -5ainxX + -5ainx2 + 5ainx2 + -100ai2n + 100ai2n + -25ai2nx + 25ai2nx + 36an + -36an + -12anX + 12anX + -3anx + 3anx + 1anxX + -1anxX + -3anx2 + 3anx2 + anx2X + -1anx2X

Combine like terms: 5ainxX + -5ainxX = 0
-20ainX + 20ainx + -5ainxX + 5ainx2 + 100ai2n + 25ai2nx + -36an + 12anX + 3anx + -1anxX + 3anx2 + -1anx2X + xF = 0 + -5ainx2 + 5ainx2 + -100ai2n + 100ai2n + -25ai2nx + 25ai2nx + 36an + -36an + -12anX + 12anX + -3anx + 3anx + 1anxX + -1anxX + -3anx2 + 3anx2 + anx2X + -1anx2X
-20ainX + 20ainx + -5ainxX + 5ainx2 + 100ai2n + 25ai2nx + -36an + 12anX + 3anx + -1anxX + 3anx2 + -1anx2X + xF = -5ainx2 + 5ainx2 + -100ai2n + 100ai2n + -25ai2nx + 25ai2nx + 36an + -36an + -12anX + 12anX + -3anx + 3anx + 1anxX + -1anxX + -3anx2 + 3anx2 + anx2X + -1anx2X

Combine like terms: -5ainx2 + 5ainx2 = 0
-20ainX + 20ainx + -5ainxX + 5ainx2 + 100ai2n + 25ai2nx + -36an + 12anX + 3anx + -1anxX + 3anx2 + -1anx2X + xF = 0 + -100ai2n + 100ai2n + -25ai2nx + 25ai2nx + 36an + -36an + -12anX + 12anX + -3anx + 3anx + 1anxX + -1anxX + -3anx2 + 3anx2 + anx2X + -1anx2X
-20ainX + 20ainx + -5ainxX + 5ainx2 + 100ai2n + 25ai2nx + -36an + 12anX + 3anx + -1anxX + 3anx2 + -1anx2X + xF = -100ai2n + 100ai2n + -25ai2nx + 25ai2nx + 36an + -36an + -12anX + 12anX + -3anx + 3anx + 1anxX + -1anxX + -3anx2 + 3anx2 + anx2X + -1anx2X

Combine like terms: -100ai2n + 100ai2n = 0
-20ainX + 20ainx + -5ainxX + 5ainx2 + 100ai2n + 25ai2nx + -36an + 12anX + 3anx + -1anxX + 3anx2 + -1anx2X + xF = 0 + -25ai2nx + 25ai2nx + 36an + -36an + -12anX + 12anX + -3anx + 3anx + 1anxX + -1anxX + -3anx2 + 3anx2 + anx2X + -1anx2X
-20ainX + 20ainx + -5ainxX + 5ainx2 + 100ai2n + 25ai2nx + -36an + 12anX + 3anx + -1anxX + 3anx2 + -1anx2X + xF = -25ai2nx + 25ai2nx + 36an + -36an + -12anX + 12anX + -3anx + 3anx + 1anxX + -1anxX + -3anx2 + 3anx2 + anx2X + -1anx2X

Combine like terms: -25ai2nx + 25ai2nx = 0
-20ainX + 20ainx + -5ainxX + 5ainx2 + 100ai2n + 25ai2nx + -36an + 12anX + 3anx + -1anxX + 3anx2 + -1anx2X + xF = 0 + 36an + -36an + -12anX + 12anX + -3anx + 3anx + 1anxX + -1anxX + -3anx2 + 3anx2 + anx2X + -1anx2X
-20ainX + 20ainx + -5ainxX + 5ainx2 + 100ai2n + 25ai2nx + -36an + 12anX + 3anx + -1anxX + 3anx2 + -1anx2X + xF = 36an + -36an + -12anX + 12anX + -3anx + 3anx + 1anxX + -1anxX + -3anx2 + 3anx2 + anx2X + -1anx2X

Combine like terms: 36an + -36an = 0
-20ainX + 20ainx + -5ainxX + 5ainx2 + 100ai2n + 25ai2nx + -36an + 12anX + 3anx + -1anxX + 3anx2 + -1anx2X + xF = 0 + -12anX + 12anX + -3anx + 3anx + 1anxX + -1anxX + -3anx2 + 3anx2 + anx2X + -1anx2X
-20ainX + 20ainx + -5ainxX + 5ainx2 + 100ai2n + 25ai2nx + -36an + 12anX + 3anx + -1anxX + 3anx2 + -1anx2X + xF = -12anX + 12anX + -3anx + 3anx + 1anxX + -1anxX + -3anx2 + 3anx2 + anx2X + -1anx2X

Combine like terms: -12anX + 12anX = 0
-20ainX + 20ainx + -5ainxX + 5ainx2 + 100ai2n + 25ai2nx + -36an + 12anX + 3anx + -1anxX + 3anx2 + -1anx2X + xF = 0 + -3anx + 3anx + 1anxX + -1anxX + -3anx2 + 3anx2 + anx2X + -1anx2X
-20ainX + 20ainx + -5ainxX + 5ainx2 + 100ai2n + 25ai2nx + -36an + 12anX + 3anx + -1anxX + 3anx2 + -1anx2X + xF = -3anx + 3anx + 1anxX + -1anxX + -3anx2 + 3anx2 + anx2X + -1anx2X

Combine like terms: -3anx + 3anx = 0
-20ainX + 20ainx + -5ainxX + 5ainx2 + 100ai2n + 25ai2nx + -36an + 12anX + 3anx + -1anxX + 3anx2 + -1anx2X + xF = 0 + 1anxX + -1anxX + -3anx2 + 3anx2 + anx2X + -1anx2X
-20ainX + 20ainx + -5ainxX + 5ainx2 + 100ai2n + 25ai2nx + -36an + 12anX + 3anx + -1anxX + 3anx2 + -1anx2X + xF = 1anxX + -1anxX + -3anx2 + 3anx2 + anx2X + -1anx2X

Combine like terms: 1anxX + -1anxX = 0
-20ainX + 20ainx + -5ainxX + 5ainx2 + 100ai2n + 25ai2nx + -36an + 12anX + 3anx + -1anxX + 3anx2 + -1anx2X + xF = 0 + -3anx2 + 3anx2 + anx2X + -1anx2X
-20ainX + 20ainx + -5ainxX + 5ainx2 + 100ai2n + 25ai2nx + -36an + 12anX + 3anx + -1anxX + 3anx2 + -1anx2X + xF = -3anx2 + 3anx2 + anx2X + -1anx2X

Combine like terms: -3anx2 + 3anx2 = 0
-20ainX + 20ainx + -5ainxX + 5ainx2 + 100ai2n + 25ai2nx + -36an + 12anX + 3anx + -1anxX + 3anx2 + -1anx2X + xF = 0 + anx2X + -1anx2X
-20ainX + 20ainx + -5ainxX + 5ainx2 + 100ai2n + 25ai2nx + -36an + 12anX + 3anx + -1anxX + 3anx2 + -1anx2X + xF = anx2X + -1anx2X

Combine like terms: anx2X + -1anx2X = 0
-20ainX + 20ainx + -5ainxX + 5ainx2 + 100ai2n + 25ai2nx + -36an + 12anX + 3anx + -1anxX + 3anx2 + -1anx2X + xF = 0

The solution to this equation could not be determined.

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