f(x)=(x+5)(x+1)(x-2)(x-3)

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Solution for f(x)=(x+5)(x+1)(x-2)(x-3) equation: 


Simplifying
f(x) = (x + 5)(x + 1)(x + -2)(x + -3)

Multiply f * x
fx = (x + 5)(x + 1)(x + -2)(x + -3)

Reorder the terms:
fx = (5 + x)(x + 1)(x + -2)(x + -3)

Reorder the terms:
fx = (5 + x)(1 + x)(x + -2)(x + -3)

Reorder the terms:
fx = (5 + x)(1 + x)(-2 + x)(x + -3)

Reorder the terms:
fx = (5 + x)(1 + x)(-2 + x)(-3 + x)

Multiply (5 + x) * (1 + x)
fx = (5(1 + x) + x(1 + x))(-2 + x)(-3 + x)
fx = ((1 * 5 + x * 5) + x(1 + x))(-2 + x)(-3 + x)
fx = ((5 + 5x) + x(1 + x))(-2 + x)(-3 + x)
fx = (5 + 5x + (1 * x + x * x))(-2 + x)(-3 + x)
fx = (5 + 5x + (1x + x2))(-2 + x)(-3 + x)

Combine like terms: 5x + 1x = 6x
fx = (5 + 6x + x2)(-2 + x)(-3 + x)

Multiply (5 + 6x + x2) * (-2 + x)
fx = (5(-2 + x) + 6x * (-2 + x) + x2(-2 + x))(-3 + x)
fx = ((-2 * 5 + x * 5) + 6x * (-2 + x) + x2(-2 + x))(-3 + x)
fx = ((-10 + 5x) + 6x * (-2 + x) + x2(-2 + x))(-3 + x)
fx = (-10 + 5x + (-2 * 6x + x * 6x) + x2(-2 + x))(-3 + x)
fx = (-10 + 5x + (-12x + 6x2) + x2(-2 + x))(-3 + x)
fx = (-10 + 5x + -12x + 6x2 + (-2 * x2 + x * x2))(-3 + x)
fx = (-10 + 5x + -12x + 6x2 + (-2x2 + x3))(-3 + x)

Combine like terms: 5x + -12x = -7x
fx = (-10 + -7x + 6x2 + -2x2 + x3)(-3 + x)

Combine like terms: 6x2 + -2x2 = 4x2
fx = (-10 + -7x + 4x2 + x3)(-3 + x)

Multiply (-10 + -7x + 4x2 + x3) * (-3 + x)
fx = (-10(-3 + x) + -7x * (-3 + x) + 4x2 * (-3 + x) + x3(-3 + x))
fx = ((-3 * -10 + x * -10) + -7x * (-3 + x) + 4x2 * (-3 + x) + x3(-3 + x))
fx = ((30 + -10x) + -7x * (-3 + x) + 4x2 * (-3 + x) + x3(-3 + x))
fx = (30 + -10x + (-3 * -7x + x * -7x) + 4x2 * (-3 + x) + x3(-3 + x))
fx = (30 + -10x + (21x + -7x2) + 4x2 * (-3 + x) + x3(-3 + x))
fx = (30 + -10x + 21x + -7x2 + (-3 * 4x2 + x * 4x2) + x3(-3 + x))
fx = (30 + -10x + 21x + -7x2 + (-12x2 + 4x3) + x3(-3 + x))
fx = (30 + -10x + 21x + -7x2 + -12x2 + 4x3 + (-3 * x3 + x * x3))
fx = (30 + -10x + 21x + -7x2 + -12x2 + 4x3 + (-3x3 + x4))

Combine like terms: -10x + 21x = 11x
fx = (30 + 11x + -7x2 + -12x2 + 4x3 + -3x3 + x4)

Combine like terms: -7x2 + -12x2 = -19x2
fx = (30 + 11x + -19x2 + 4x3 + -3x3 + x4)

Combine like terms: 4x3 + -3x3 = 1x3
fx = (30 + 11x + -19x2 + 1x3 + x4)

Solving
fx = 30 + 11x + -19x2 + 1x3 + x4

Solving for variable 'f'.

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

Divide each side by 'x'.
f = 30x-1 + 11 + -19x + x2 + x3

Simplifying
f = 30x-1 + 11 + -19x + x2 + x3

Reorder the terms:
f = 11 + 30x-1 + -19x + x2 + x3

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