k(x)=2i(4-x)(5-x)(6-x)

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Solution for k(x)=2i(4-x)(5-x)(6-x) equation: 


Simplifying
k(x) = 2i(4 + -1x)(5 + -1x)(6 + -1x)

Multiply k * x
kx = 2i(4 + -1x)(5 + -1x)(6 + -1x)

Multiply (4 + -1x) * (5 + -1x)
kx = 2i(4(5 + -1x) + -1x * (5 + -1x))(6 + -1x)
kx = 2i((5 * 4 + -1x * 4) + -1x * (5 + -1x))(6 + -1x)
kx = 2i((20 + -4x) + -1x * (5 + -1x))(6 + -1x)
kx = 2i(20 + -4x + (5 * -1x + -1x * -1x))(6 + -1x)
kx = 2i(20 + -4x + (-5x + 1x2))(6 + -1x)

Combine like terms: -4x + -5x = -9x
kx = 2i(20 + -9x + 1x2)(6 + -1x)

Multiply (20 + -9x + 1x2) * (6 + -1x)
kx = 2i(20(6 + -1x) + -9x * (6 + -1x) + 1x2 * (6 + -1x))
kx = 2i((6 * 20 + -1x * 20) + -9x * (6 + -1x) + 1x2 * (6 + -1x))
kx = 2i((120 + -20x) + -9x * (6 + -1x) + 1x2 * (6 + -1x))
kx = 2i(120 + -20x + (6 * -9x + -1x * -9x) + 1x2 * (6 + -1x))
kx = 2i(120 + -20x + (-54x + 9x2) + 1x2 * (6 + -1x))
kx = 2i(120 + -20x + -54x + 9x2 + (6 * 1x2 + -1x * 1x2))
kx = 2i(120 + -20x + -54x + 9x2 + (6x2 + -1x3))

Combine like terms: -20x + -54x = -74x
kx = 2i(120 + -74x + 9x2 + 6x2 + -1x3)

Combine like terms: 9x2 + 6x2 = 15x2
kx = 2i(120 + -74x + 15x2 + -1x3)
kx = (120 * 2i + -74x * 2i + 15x2 * 2i + -1x3 * 2i)
kx = (240i + -148ix + 30ix2 + -2ix3)

Solving
kx = 240i + -148ix + 30ix2 + -2ix3

Solving for variable 'k'.

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

Divide each side by 'x'.
k = 240ix-1 + -148i + 30ix + -2ix2

Simplifying
k = 240ix-1 + -148i + 30ix + -2ix2

Reorder the terms:
k = -148i + 240ix-1 + 30ix + -2ix2

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