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

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


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

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

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

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

Multiply (4 + x) * (3 + -2x)
fx = (4(3 + -2x) + x(3 + -2x))(1 + x)
fx = ((3 * 4 + -2x * 4) + x(3 + -2x))(1 + x)
fx = ((12 + -8x) + x(3 + -2x))(1 + x)
fx = (12 + -8x + (3 * x + -2x * x))(1 + x)
fx = (12 + -8x + (3x + -2x2))(1 + x)

Combine like terms: -8x + 3x = -5x
fx = (12 + -5x + -2x2)(1 + x)

Multiply (12 + -5x + -2x2) * (1 + x)
fx = (12(1 + x) + -5x * (1 + x) + -2x2 * (1 + x))
fx = ((1 * 12 + x * 12) + -5x * (1 + x) + -2x2 * (1 + x))
fx = ((12 + 12x) + -5x * (1 + x) + -2x2 * (1 + x))
fx = (12 + 12x + (1 * -5x + x * -5x) + -2x2 * (1 + x))
fx = (12 + 12x + (-5x + -5x2) + -2x2 * (1 + x))
fx = (12 + 12x + -5x + -5x2 + (1 * -2x2 + x * -2x2))
fx = (12 + 12x + -5x + -5x2 + (-2x2 + -2x3))

Combine like terms: 12x + -5x = 7x
fx = (12 + 7x + -5x2 + -2x2 + -2x3)

Combine like terms: -5x2 + -2x2 = -7x2
fx = (12 + 7x + -7x2 + -2x3)

Solving
fx = 12 + 7x + -7x2 + -2x3

Solving for variable 'f'.

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

Divide each side by 'x'.
f = 12x-1 + 7 + -7x + -2x2

Simplifying
f = 12x-1 + 7 + -7x + -2x2

Reorder the terms:
f = 7 + 12x-1 + -7x + -2x2

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