f(x)=(2x+3)(7x+2)(13x+7)(x+13)

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Solution for f(x)=(2x+3)(7x+2)(13x+7)(x+13) equation: 


Simplifying
f(x) = (2x + 3)(7x + 2)(13x + 7)(x + 13)

Multiply f * x
fx = (2x + 3)(7x + 2)(13x + 7)(x + 13)

Reorder the terms:
fx = (3 + 2x)(7x + 2)(13x + 7)(x + 13)

Reorder the terms:
fx = (3 + 2x)(2 + 7x)(13x + 7)(x + 13)

Reorder the terms:
fx = (3 + 2x)(2 + 7x)(7 + 13x)(x + 13)

Reorder the terms:
fx = (3 + 2x)(2 + 7x)(7 + 13x)(13 + x)

Multiply (3 + 2x) * (2 + 7x)
fx = (3(2 + 7x) + 2x * (2 + 7x))(7 + 13x)(13 + x)
fx = ((2 * 3 + 7x * 3) + 2x * (2 + 7x))(7 + 13x)(13 + x)
fx = ((6 + 21x) + 2x * (2 + 7x))(7 + 13x)(13 + x)
fx = (6 + 21x + (2 * 2x + 7x * 2x))(7 + 13x)(13 + x)
fx = (6 + 21x + (4x + 14x2))(7 + 13x)(13 + x)

Combine like terms: 21x + 4x = 25x
fx = (6 + 25x + 14x2)(7 + 13x)(13 + x)

Multiply (6 + 25x + 14x2) * (7 + 13x)
fx = (6(7 + 13x) + 25x * (7 + 13x) + 14x2 * (7 + 13x))(13 + x)
fx = ((7 * 6 + 13x * 6) + 25x * (7 + 13x) + 14x2 * (7 + 13x))(13 + x)
fx = ((42 + 78x) + 25x * (7 + 13x) + 14x2 * (7 + 13x))(13 + x)
fx = (42 + 78x + (7 * 25x + 13x * 25x) + 14x2 * (7 + 13x))(13 + x)
fx = (42 + 78x + (175x + 325x2) + 14x2 * (7 + 13x))(13 + x)
fx = (42 + 78x + 175x + 325x2 + (7 * 14x2 + 13x * 14x2))(13 + x)
fx = (42 + 78x + 175x + 325x2 + (98x2 + 182x3))(13 + x)

Combine like terms: 78x + 175x = 253x
fx = (42 + 253x + 325x2 + 98x2 + 182x3)(13 + x)

Combine like terms: 325x2 + 98x2 = 423x2
fx = (42 + 253x + 423x2 + 182x3)(13 + x)

Multiply (42 + 253x + 423x2 + 182x3) * (13 + x)
fx = (42(13 + x) + 253x * (13 + x) + 423x2 * (13 + x) + 182x3 * (13 + x))
fx = ((13 * 42 + x * 42) + 253x * (13 + x) + 423x2 * (13 + x) + 182x3 * (13 + x))
fx = ((546 + 42x) + 253x * (13 + x) + 423x2 * (13 + x) + 182x3 * (13 + x))
fx = (546 + 42x + (13 * 253x + x * 253x) + 423x2 * (13 + x) + 182x3 * (13 + x))
fx = (546 + 42x + (3289x + 253x2) + 423x2 * (13 + x) + 182x3 * (13 + x))
fx = (546 + 42x + 3289x + 253x2 + (13 * 423x2 + x * 423x2) + 182x3 * (13 + x))
fx = (546 + 42x + 3289x + 253x2 + (5499x2 + 423x3) + 182x3 * (13 + x))
fx = (546 + 42x + 3289x + 253x2 + 5499x2 + 423x3 + (13 * 182x3 + x * 182x3))
fx = (546 + 42x + 3289x + 253x2 + 5499x2 + 423x3 + (2366x3 + 182x4))

Combine like terms: 42x + 3289x = 3331x
fx = (546 + 3331x + 253x2 + 5499x2 + 423x3 + 2366x3 + 182x4)

Combine like terms: 253x2 + 5499x2 = 5752x2
fx = (546 + 3331x + 5752x2 + 423x3 + 2366x3 + 182x4)

Combine like terms: 423x3 + 2366x3 = 2789x3
fx = (546 + 3331x + 5752x2 + 2789x3 + 182x4)

Solving
fx = 546 + 3331x + 5752x2 + 2789x3 + 182x4

Solving for variable 'f'.

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

Divide each side by 'x'.
f = 546x-1 + 3331 + 5752x + 2789x2 + 182x3

Simplifying
f = 546x-1 + 3331 + 5752x + 2789x2 + 182x3

Reorder the terms:
f = 3331 + 546x-1 + 5752x + 2789x2 + 182x3

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