h(x)=0.25x(x+2)(x-3)(x-4)(x+5)

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Solution for h(x)=0.25x(x+2)(x-3)(x-4)(x+5) equation: 


Simplifying
h(x) = 0.25x(x + 2)(x + -3)(x + -4)(x + 5)

Multiply h * x
hx = 0.25x(x + 2)(x + -3)(x + -4)(x + 5)

Reorder the terms:
hx = 0.25x(2 + x)(x + -3)(x + -4)(x + 5)

Reorder the terms:
hx = 0.25x(2 + x)(-3 + x)(x + -4)(x + 5)

Reorder the terms:
hx = 0.25x(2 + x)(-3 + x)(-4 + x)(x + 5)

Reorder the terms:
hx = 0.25x(2 + x)(-3 + x)(-4 + x)(5 + x)

Multiply (2 + x) * (-3 + x)
hx = 0.25x(2(-3 + x) + x(-3 + x))(-4 + x)(5 + x)
hx = 0.25x((-3 * 2 + x * 2) + x(-3 + x))(-4 + x)(5 + x)
hx = 0.25x((-6 + 2x) + x(-3 + x))(-4 + x)(5 + x)
hx = 0.25x(-6 + 2x + (-3 * x + x * x))(-4 + x)(5 + x)
hx = 0.25x(-6 + 2x + (-3x + x2))(-4 + x)(5 + x)

Combine like terms: 2x + -3x = -1x
hx = 0.25x(-6 + -1x + x2)(-4 + x)(5 + x)

Multiply (-6 + -1x + x2) * (-4 + x)
hx = 0.25x(-6(-4 + x) + -1x * (-4 + x) + x2(-4 + x))(5 + x)
hx = 0.25x((-4 * -6 + x * -6) + -1x * (-4 + x) + x2(-4 + x))(5 + x)
hx = 0.25x((24 + -6x) + -1x * (-4 + x) + x2(-4 + x))(5 + x)
hx = 0.25x(24 + -6x + (-4 * -1x + x * -1x) + x2(-4 + x))(5 + x)
hx = 0.25x(24 + -6x + (4x + -1x2) + x2(-4 + x))(5 + x)
hx = 0.25x(24 + -6x + 4x + -1x2 + (-4 * x2 + x * x2))(5 + x)
hx = 0.25x(24 + -6x + 4x + -1x2 + (-4x2 + x3))(5 + x)

Combine like terms: -6x + 4x = -2x
hx = 0.25x(24 + -2x + -1x2 + -4x2 + x3)(5 + x)

Combine like terms: -1x2 + -4x2 = -5x2
hx = 0.25x(24 + -2x + -5x2 + x3)(5 + x)

Multiply (24 + -2x + -5x2 + x3) * (5 + x)
hx = 0.25x(24(5 + x) + -2x * (5 + x) + -5x2 * (5 + x) + x3(5 + x))
hx = 0.25x((5 * 24 + x * 24) + -2x * (5 + x) + -5x2 * (5 + x) + x3(5 + x))
hx = 0.25x((120 + 24x) + -2x * (5 + x) + -5x2 * (5 + x) + x3(5 + x))
hx = 0.25x(120 + 24x + (5 * -2x + x * -2x) + -5x2 * (5 + x) + x3(5 + x))
hx = 0.25x(120 + 24x + (-10x + -2x2) + -5x2 * (5 + x) + x3(5 + x))
hx = 0.25x(120 + 24x + -10x + -2x2 + (5 * -5x2 + x * -5x2) + x3(5 + x))
hx = 0.25x(120 + 24x + -10x + -2x2 + (-25x2 + -5x3) + x3(5 + x))
hx = 0.25x(120 + 24x + -10x + -2x2 + -25x2 + -5x3 + (5 * x3 + x * x3))
hx = 0.25x(120 + 24x + -10x + -2x2 + -25x2 + -5x3 + (5x3 + x4))

Combine like terms: 24x + -10x = 14x
hx = 0.25x(120 + 14x + -2x2 + -25x2 + -5x3 + 5x3 + x4)

Combine like terms: -2x2 + -25x2 = -27x2
hx = 0.25x(120 + 14x + -27x2 + -5x3 + 5x3 + x4)

Combine like terms: -5x3 + 5x3 = 0
hx = 0.25x(120 + 14x + -27x2 + 0 + x4)
hx = 0.25x(120 + 14x + -27x2 + x4)
hx = (120 * 0.25x + 14x * 0.25x + -27x2 * 0.25x + x4 * 0.25x)
hx = (30x + 3.5x2 + -6.75x3 + 0.25x5)

Solving
hx = 30x + 3.5x2 + -6.75x3 + 0.25x5

Solving for variable 'h'.

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

Divide each side by 'x'.
h = 30 + 3.5x + -6.75x2 + 0.25x4

Simplifying
h = 30 + 3.5x + -6.75x2 + 0.25x4

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