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

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


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

Multiply g * x
gx = (x + -1)(x + -5)(x + 2)(x + 3)

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

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

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

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

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

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

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

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

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

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

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

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

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

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

Solving for variable 'g'.

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

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

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

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

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