f(x)=(x-4)(x+3)(x-1)(2x-12)

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Solution for f(x)=(x-4)(x+3)(x-1)(2x-12) equation: 


Simplifying
f(x) = (x + -4)(x + 3)(x + -1)(2x + -12)

Multiply f * x
fx = (x + -4)(x + 3)(x + -1)(2x + -12)

Reorder the terms:
fx = (-4 + x)(x + 3)(x + -1)(2x + -12)

Reorder the terms:
fx = (-4 + x)(3 + x)(x + -1)(2x + -12)

Reorder the terms:
fx = (-4 + x)(3 + x)(-1 + x)(2x + -12)

Reorder the terms:
fx = (-4 + x)(3 + x)(-1 + x)(-12 + 2x)

Multiply (-4 + x) * (3 + x)
fx = (-4(3 + x) + x(3 + x))(-1 + x)(-12 + 2x)
fx = ((3 * -4 + x * -4) + x(3 + x))(-1 + x)(-12 + 2x)
fx = ((-12 + -4x) + x(3 + x))(-1 + x)(-12 + 2x)
fx = (-12 + -4x + (3 * x + x * x))(-1 + x)(-12 + 2x)
fx = (-12 + -4x + (3x + x2))(-1 + x)(-12 + 2x)

Combine like terms: -4x + 3x = -1x
fx = (-12 + -1x + x2)(-1 + x)(-12 + 2x)

Multiply (-12 + -1x + x2) * (-1 + x)
fx = (-12(-1 + x) + -1x * (-1 + x) + x2(-1 + x))(-12 + 2x)
fx = ((-1 * -12 + x * -12) + -1x * (-1 + x) + x2(-1 + x))(-12 + 2x)
fx = ((12 + -12x) + -1x * (-1 + x) + x2(-1 + x))(-12 + 2x)
fx = (12 + -12x + (-1 * -1x + x * -1x) + x2(-1 + x))(-12 + 2x)
fx = (12 + -12x + (1x + -1x2) + x2(-1 + x))(-12 + 2x)
fx = (12 + -12x + 1x + -1x2 + (-1 * x2 + x * x2))(-12 + 2x)
fx = (12 + -12x + 1x + -1x2 + (-1x2 + x3))(-12 + 2x)

Combine like terms: -12x + 1x = -11x
fx = (12 + -11x + -1x2 + -1x2 + x3)(-12 + 2x)

Combine like terms: -1x2 + -1x2 = -2x2
fx = (12 + -11x + -2x2 + x3)(-12 + 2x)

Multiply (12 + -11x + -2x2 + x3) * (-12 + 2x)
fx = (12(-12 + 2x) + -11x * (-12 + 2x) + -2x2 * (-12 + 2x) + x3(-12 + 2x))
fx = ((-12 * 12 + 2x * 12) + -11x * (-12 + 2x) + -2x2 * (-12 + 2x) + x3(-12 + 2x))
fx = ((-144 + 24x) + -11x * (-12 + 2x) + -2x2 * (-12 + 2x) + x3(-12 + 2x))
fx = (-144 + 24x + (-12 * -11x + 2x * -11x) + -2x2 * (-12 + 2x) + x3(-12 + 2x))
fx = (-144 + 24x + (132x + -22x2) + -2x2 * (-12 + 2x) + x3(-12 + 2x))
fx = (-144 + 24x + 132x + -22x2 + (-12 * -2x2 + 2x * -2x2) + x3(-12 + 2x))
fx = (-144 + 24x + 132x + -22x2 + (24x2 + -4x3) + x3(-12 + 2x))
fx = (-144 + 24x + 132x + -22x2 + 24x2 + -4x3 + (-12 * x3 + 2x * x3))
fx = (-144 + 24x + 132x + -22x2 + 24x2 + -4x3 + (-12x3 + 2x4))

Combine like terms: 24x + 132x = 156x
fx = (-144 + 156x + -22x2 + 24x2 + -4x3 + -12x3 + 2x4)

Combine like terms: -22x2 + 24x2 = 2x2
fx = (-144 + 156x + 2x2 + -4x3 + -12x3 + 2x4)

Combine like terms: -4x3 + -12x3 = -16x3
fx = (-144 + 156x + 2x2 + -16x3 + 2x4)

Solving
fx = -144 + 156x + 2x2 + -16x3 + 2x4

Solving for variable 'f'.

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

Divide each side by 'x'.
f = -144x-1 + 156 + 2x + -16x2 + 2x3

Simplifying
f = -144x-1 + 156 + 2x + -16x2 + 2x3

Reorder the terms:
f = 156 + -144x-1 + 2x + -16x2 + 2x3

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