f(x)=(X+3)(x-3)(x+12)(x-12)(x+5)

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Solution for f(x)=(X+3)(x-3)(x+12)(x-12)(x+5) equation: 


Simplifying
f(x) = (X + 3)(x + -3)(x + 12)(x + -12)(x + 5)

Multiply f * x
fx = (X + 3)(x + -3)(x + 12)(x + -12)(x + 5)

Reorder the terms:
fx = (3 + X)(x + -3)(x + 12)(x + -12)(x + 5)

Reorder the terms:
fx = (3 + X)(-3 + x)(x + 12)(x + -12)(x + 5)

Reorder the terms:
fx = (3 + X)(-3 + x)(12 + x)(x + -12)(x + 5)

Reorder the terms:
fx = (3 + X)(-3 + x)(12 + x)(-12 + x)(x + 5)

Reorder the terms:
fx = (3 + X)(-3 + x)(12 + x)(-12 + x)(5 + x)

Multiply (3 + X) * (-3 + x)
fx = (3(-3 + x) + X(-3 + x))(12 + x)(-12 + x)(5 + x)
fx = ((-3 * 3 + x * 3) + X(-3 + x))(12 + x)(-12 + x)(5 + x)
fx = ((-9 + 3x) + X(-3 + x))(12 + x)(-12 + x)(5 + x)
fx = (-9 + 3x + (-3 * X + x * X))(12 + x)(-12 + x)(5 + x)
fx = (-9 + 3x + (-3X + xX))(12 + x)(-12 + x)(5 + x)

Reorder the terms:
fx = (-9 + -3X + 3x + xX)(12 + x)(-12 + x)(5 + x)
fx = (-9 + -3X + 3x + xX)(12 + x)(-12 + x)(5 + x)

Multiply (-9 + -3X + 3x + xX) * (12 + x)
fx = (-9(12 + x) + -3X * (12 + x) + 3x * (12 + x) + xX(12 + x))(-12 + x)(5 + x)
fx = ((12 * -9 + x * -9) + -3X * (12 + x) + 3x * (12 + x) + xX(12 + x))(-12 + x)(5 + x)
fx = ((-108 + -9x) + -3X * (12 + x) + 3x * (12 + x) + xX(12 + x))(-12 + x)(5 + x)
fx = (-108 + -9x + (12 * -3X + x * -3X) + 3x * (12 + x) + xX(12 + x))(-12 + x)(5 + x)
fx = (-108 + -9x + (-36X + -3xX) + 3x * (12 + x) + xX(12 + x))(-12 + x)(5 + x)
fx = (-108 + -9x + -36X + -3xX + (12 * 3x + x * 3x) + xX(12 + x))(-12 + x)(5 + x)
fx = (-108 + -9x + -36X + -3xX + (36x + 3x2) + xX(12 + x))(-12 + x)(5 + x)
fx = (-108 + -9x + -36X + -3xX + 36x + 3x2 + (12 * xX + x * xX))(-12 + x)(5 + x)
fx = (-108 + -9x + -36X + -3xX + 36x + 3x2 + (12xX + x2X))(-12 + x)(5 + x)

Reorder the terms:
fx = (-108 + -36X + -9x + 36x + -3xX + 12xX + 3x2 + x2X)(-12 + x)(5 + x)

Combine like terms: -9x + 36x = 27x
fx = (-108 + -36X + 27x + -3xX + 12xX + 3x2 + x2X)(-12 + x)(5 + x)

Combine like terms: -3xX + 12xX = 9xX
fx = (-108 + -36X + 27x + 9xX + 3x2 + x2X)(-12 + x)(5 + x)

Multiply (-108 + -36X + 27x + 9xX + 3x2 + x2X) * (-12 + x)
fx = (-108(-12 + x) + -36X * (-12 + x) + 27x * (-12 + x) + 9xX * (-12 + x) + 3x2 * (-12 + x) + x2X(-12 + x))(5 + x)
fx = ((-12 * -108 + x * -108) + -36X * (-12 + x) + 27x * (-12 + x) + 9xX * (-12 + x) + 3x2 * (-12 + x) + x2X(-12 + x))(5 + x)
fx = ((1296 + -108x) + -36X * (-12 + x) + 27x * (-12 + x) + 9xX * (-12 + x) + 3x2 * (-12 + x) + x2X(-12 + x))(5 + x)
fx = (1296 + -108x + (-12 * -36X + x * -36X) + 27x * (-12 + x) + 9xX * (-12 + x) + 3x2 * (-12 + x) + x2X(-12 + x))(5 + x)
fx = (1296 + -108x + (432X + -36xX) + 27x * (-12 + x) + 9xX * (-12 + x) + 3x2 * (-12 + x) + x2X(-12 + x))(5 + x)
fx = (1296 + -108x + 432X + -36xX + (-12 * 27x + x * 27x) + 9xX * (-12 + x) + 3x2 * (-12 + x) + x2X(-12 + x))(5 + x)
fx = (1296 + -108x + 432X + -36xX + (-324x + 27x2) + 9xX * (-12 + x) + 3x2 * (-12 + x) + x2X(-12 + x))(5 + x)
fx = (1296 + -108x + 432X + -36xX + -324x + 27x2 + (-12 * 9xX + x * 9xX) + 3x2 * (-12 + x) + x2X(-12 + x))(5 + x)
fx = (1296 + -108x + 432X + -36xX + -324x + 27x2 + (-108xX + 9x2X) + 3x2 * (-12 + x) + x2X(-12 + x))(5 + x)
fx = (1296 + -108x + 432X + -36xX + -324x + 27x2 + -108xX + 9x2X + (-12 * 3x2 + x * 3x2) + x2X(-12 + x))(5 + x)
fx = (1296 + -108x + 432X + -36xX + -324x + 27x2 + -108xX + 9x2X + (-36x2 + 3x3) + x2X(-12 + x))(5 + x)
fx = (1296 + -108x + 432X + -36xX + -324x + 27x2 + -108xX + 9x2X + -36x2 + 3x3 + (-12 * x2X + x * x2X))(5 + x)
fx = (1296 + -108x + 432X + -36xX + -324x + 27x2 + -108xX + 9x2X + -36x2 + 3x3 + (-12x2X + x3X))(5 + x)

Reorder the terms:
fx = (1296 + 432X + -108x + -324x + -36xX + -108xX + 27x2 + -36x2 + 9x2X + -12x2X + 3x3 + x3X)(5 + x)

Combine like terms: -108x + -324x = -432x
fx = (1296 + 432X + -432x + -36xX + -108xX + 27x2 + -36x2 + 9x2X + -12x2X + 3x3 + x3X)(5 + x)

Combine like terms: -36xX + -108xX = -144xX
fx = (1296 + 432X + -432x + -144xX + 27x2 + -36x2 + 9x2X + -12x2X + 3x3 + x3X)(5 + x)

Combine like terms: 27x2 + -36x2 = -9x2
fx = (1296 + 432X + -432x + -144xX + -9x2 + 9x2X + -12x2X + 3x3 + x3X)(5 + x)

Combine like terms: 9x2X + -12x2X = -3x2X
fx = (1296 + 432X + -432x + -144xX + -9x2 + -3x2X + 3x3 + x3X)(5 + x)

Multiply (1296 + 432X + -432x + -144xX + -9x2 + -3x2X + 3x3 + x3X) * (5 + x)
fx = (1296(5 + x) + 432X * (5 + x) + -432x * (5 + x) + -144xX * (5 + x) + -9x2 * (5 + x) + -3x2X * (5 + x) + 3x3 * (5 + x) + x3X(5 + x))
fx = ((5 * 1296 + x * 1296) + 432X * (5 + x) + -432x * (5 + x) + -144xX * (5 + x) + -9x2 * (5 + x) + -3x2X * (5 + x) + 3x3 * (5 + x) + x3X(5 + x))
fx = ((6480 + 1296x) + 432X * (5 + x) + -432x * (5 + x) + -144xX * (5 + x) + -9x2 * (5 + x) + -3x2X * (5 + x) + 3x3 * (5 + x) + x3X(5 + x))
fx = (6480 + 1296x + (5 * 432X + x * 432X) + -432x * (5 + x) + -144xX * (5 + x) + -9x2 * (5 + x) + -3x2X * (5 + x) + 3x3 * (5 + x) + x3X(5 + x))
fx = (6480 + 1296x + (2160X + 432xX) + -432x * (5 + x) + -144xX * (5 + x) + -9x2 * (5 + x) + -3x2X * (5 + x) + 3x3 * (5 + x) + x3X(5 + x))
fx = (6480 + 1296x + 2160X + 432xX + (5 * -432x + x * -432x) + -144xX * (5 + x) + -9x2 * (5 + x) + -3x2X * (5 + x) + 3x3 * (5 + x) + x3X(5 + x))
fx = (6480 + 1296x + 2160X + 432xX + (-2160x + -432x2) + -144xX * (5 + x) + -9x2 * (5 + x) + -3x2X * (5 + x) + 3x3 * (5 + x) + x3X(5 + x))
fx = (6480 + 1296x + 2160X + 432xX + -2160x + -432x2 + (5 * -144xX + x * -144xX) + -9x2 * (5 + x) + -3x2X * (5 + x) + 3x3 * (5 + x) + x3X(5 + x))
fx = (6480 + 1296x + 2160X + 432xX + -2160x + -432x2 + (-720xX + -144x2X) + -9x2 * (5 + x) + -3x2X * (5 + x) + 3x3 * (5 + x) + x3X(5 + x))
fx = (6480 + 1296x + 2160X + 432xX + -2160x + -432x2 + -720xX + -144x2X + (5 * -9x2 + x * -9x2) + -3x2X * (5 + x) + 3x3 * (5 + x) + x3X(5 + x))
fx = (6480 + 1296x + 2160X + 432xX + -2160x + -432x2 + -720xX + -144x2X + (-45x2 + -9x3) + -3x2X * (5 + x) + 3x3 * (5 + x) + x3X(5 + x))
fx = (6480 + 1296x + 2160X + 432xX + -2160x + -432x2 + -720xX + -144x2X + -45x2 + -9x3 + (5 * -3x2X + x * -3x2X) + 3x3 * (5 + x) + x3X(5 + x))
fx = (6480 + 1296x + 2160X + 432xX + -2160x + -432x2 + -720xX + -144x2X + -45x2 + -9x3 + (-15x2X + -3x3X) + 3x3 * (5 + x) + x3X(5 + x))
fx = (6480 + 1296x + 2160X + 432xX + -2160x + -432x2 + -720xX + -144x2X + -45x2 + -9x3 + -15x2X + -3x3X + (5 * 3x3 + x * 3x3) + x3X(5 + x))
fx = (6480 + 1296x + 2160X + 432xX + -2160x + -432x2 + -720xX + -144x2X + -45x2 + -9x3 + -15x2X + -3x3X + (15x3 + 3x4) + x3X(5 + x))
fx = (6480 + 1296x + 2160X + 432xX + -2160x + -432x2 + -720xX + -144x2X + -45x2 + -9x3 + -15x2X + -3x3X + 15x3 + 3x4 + (5 * x3X + x * x3X))
fx = (6480 + 1296x + 2160X + 432xX + -2160x + -432x2 + -720xX + -144x2X + -45x2 + -9x3 + -15x2X + -3x3X + 15x3 + 3x4 + (5x3X + x4X))

Reorder the terms:
fx = (6480 + 2160X + 1296x + -2160x + 432xX + -720xX + -432x2 + -45x2 + -144x2X + -15x2X + -9x3 + 15x3 + -3x3X + 5x3X + 3x4 + x4X)

Combine like terms: 1296x + -2160x = -864x
fx = (6480 + 2160X + -864x + 432xX + -720xX + -432x2 + -45x2 + -144x2X + -15x2X + -9x3 + 15x3 + -3x3X + 5x3X + 3x4 + x4X)

Combine like terms: 432xX + -720xX = -288xX
fx = (6480 + 2160X + -864x + -288xX + -432x2 + -45x2 + -144x2X + -15x2X + -9x3 + 15x3 + -3x3X + 5x3X + 3x4 + x4X)

Combine like terms: -432x2 + -45x2 = -477x2
fx = (6480 + 2160X + -864x + -288xX + -477x2 + -144x2X + -15x2X + -9x3 + 15x3 + -3x3X + 5x3X + 3x4 + x4X)

Combine like terms: -144x2X + -15x2X = -159x2X
fx = (6480 + 2160X + -864x + -288xX + -477x2 + -159x2X + -9x3 + 15x3 + -3x3X + 5x3X + 3x4 + x4X)

Combine like terms: -9x3 + 15x3 = 6x3
fx = (6480 + 2160X + -864x + -288xX + -477x2 + -159x2X + 6x3 + -3x3X + 5x3X + 3x4 + x4X)

Combine like terms: -3x3X + 5x3X = 2x3X
fx = (6480 + 2160X + -864x + -288xX + -477x2 + -159x2X + 6x3 + 2x3X + 3x4 + x4X)

Solving
fx = 6480 + 2160X + -864x + -288xX + -477x2 + -159x2X + 6x3 + 2x3X + 3x4 + x4X

Solving for variable 'f'.

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

Divide each side by 'x'.
f = 6480x-1 + 2160x-1X + -864 + -288X + -477x + -159xX + 6x2 + 2x2X + 3x3 + x3X

Simplifying
f = 6480x-1 + 2160x-1X + -864 + -288X + -477x + -159xX + 6x2 + 2x2X + 3x3 + x3X

Reorder the terms:
f = -864 + -288X + 6480x-1 + 2160x-1X + -477x + -159xX + 6x2 + 2x2X + 3x3 + x3X

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