f(x)=-(x-1)(x-1.5)(x-.5)(x+.5)(X+1)(x+1.5)

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Solution for f(x)=-(x-1)(x-1.5)(x-.5)(x+.5)(X+1)(x+1.5) equation: 


Simplifying
f(x) = -1(x + -1)(x + -1.5)(x + -0.5)(x + 0.5)(X + 1)(x + 1.5)

Multiply f * x
fx = -1(x + -1)(x + -1.5)(x + -0.5)(x + 0.5)(X + 1)(x + 1.5)

Reorder the terms:
fx = -1(-1 + x)(x + -1.5)(x + -0.5)(x + 0.5)(X + 1)(x + 1.5)

Reorder the terms:
fx = -1(-1 + x)(-1.5 + x)(x + -0.5)(x + 0.5)(X + 1)(x + 1.5)

Reorder the terms:
fx = -1(-1 + x)(-1.5 + x)(-0.5 + x)(x + 0.5)(X + 1)(x + 1.5)

Reorder the terms:
fx = -1(-1 + x)(-1.5 + x)(-0.5 + x)(0.5 + x)(X + 1)(x + 1.5)

Reorder the terms:
fx = -1(-1 + x)(-1.5 + x)(-0.5 + x)(0.5 + x)(1 + X)(x + 1.5)

Reorder the terms:
fx = -1(-1 + x)(-1.5 + x)(-0.5 + x)(0.5 + x)(1 + X)(1.5 + x)

Multiply (-1 + x) * (-1.5 + x)
fx = -1(-1(-1.5 + x) + x(-1.5 + x))(-0.5 + x)(0.5 + x)(1 + X)(1.5 + x)
fx = -1((-1.5 * -1 + x * -1) + x(-1.5 + x))(-0.5 + x)(0.5 + x)(1 + X)(1.5 + x)
fx = -1((1.5 + -1x) + x(-1.5 + x))(-0.5 + x)(0.5 + x)(1 + X)(1.5 + x)
fx = -1(1.5 + -1x + (-1.5 * x + x * x))(-0.5 + x)(0.5 + x)(1 + X)(1.5 + x)
fx = -1(1.5 + -1x + (-1.5x + x2))(-0.5 + x)(0.5 + x)(1 + X)(1.5 + x)

Combine like terms: -1x + -1.5x = -2.5x
fx = -1(1.5 + -2.5x + x2)(-0.5 + x)(0.5 + x)(1 + X)(1.5 + x)

Multiply (1.5 + -2.5x + x2) * (-0.5 + x)
fx = -1(1.5(-0.5 + x) + -2.5x * (-0.5 + x) + x2(-0.5 + x))(0.5 + x)(1 + X)(1.5 + x)
fx = -1((-0.5 * 1.5 + x * 1.5) + -2.5x * (-0.5 + x) + x2(-0.5 + x))(0.5 + x)(1 + X)(1.5 + x)
fx = -1((-0.75 + 1.5x) + -2.5x * (-0.5 + x) + x2(-0.5 + x))(0.5 + x)(1 + X)(1.5 + x)
fx = -1(-0.75 + 1.5x + (-0.5 * -2.5x + x * -2.5x) + x2(-0.5 + x))(0.5 + x)(1 + X)(1.5 + x)
fx = -1(-0.75 + 1.5x + (1.25x + -2.5x2) + x2(-0.5 + x))(0.5 + x)(1 + X)(1.5 + x)
fx = -1(-0.75 + 1.5x + 1.25x + -2.5x2 + (-0.5 * x2 + x * x2))(0.5 + x)(1 + X)(1.5 + x)
fx = -1(-0.75 + 1.5x + 1.25x + -2.5x2 + (-0.5x2 + x3))(0.5 + x)(1 + X)(1.5 + x)

Combine like terms: 1.5x + 1.25x = 2.75x
fx = -1(-0.75 + 2.75x + -2.5x2 + -0.5x2 + x3)(0.5 + x)(1 + X)(1.5 + x)

Combine like terms: -2.5x2 + -0.5x2 = -3x2
fx = -1(-0.75 + 2.75x + -3x2 + x3)(0.5 + x)(1 + X)(1.5 + x)

Multiply (-0.75 + 2.75x + -3x2 + x3) * (0.5 + x)
fx = -1(-0.75(0.5 + x) + 2.75x * (0.5 + x) + -3x2 * (0.5 + x) + x3(0.5 + x))(1 + X)(1.5 + x)
fx = -1((0.5 * -0.75 + x * -0.75) + 2.75x * (0.5 + x) + -3x2 * (0.5 + x) + x3(0.5 + x))(1 + X)(1.5 + x)
fx = -1((-0.375 + -0.75x) + 2.75x * (0.5 + x) + -3x2 * (0.5 + x) + x3(0.5 + x))(1 + X)(1.5 + x)
fx = -1(-0.375 + -0.75x + (0.5 * 2.75x + x * 2.75x) + -3x2 * (0.5 + x) + x3(0.5 + x))(1 + X)(1.5 + x)
fx = -1(-0.375 + -0.75x + (1.375x + 2.75x2) + -3x2 * (0.5 + x) + x3(0.5 + x))(1 + X)(1.5 + x)
fx = -1(-0.375 + -0.75x + 1.375x + 2.75x2 + (0.5 * -3x2 + x * -3x2) + x3(0.5 + x))(1 + X)(1.5 + x)
fx = -1(-0.375 + -0.75x + 1.375x + 2.75x2 + (-1.5x2 + -3x3) + x3(0.5 + x))(1 + X)(1.5 + x)
fx = -1(-0.375 + -0.75x + 1.375x + 2.75x2 + -1.5x2 + -3x3 + (0.5 * x3 + x * x3))(1 + X)(1.5 + x)
fx = -1(-0.375 + -0.75x + 1.375x + 2.75x2 + -1.5x2 + -3x3 + (0.5x3 + x4))(1 + X)(1.5 + x)

Combine like terms: -0.75x + 1.375x = 0.625x
fx = -1(-0.375 + 0.625x + 2.75x2 + -1.5x2 + -3x3 + 0.5x3 + x4)(1 + X)(1.5 + x)

Combine like terms: 2.75x2 + -1.5x2 = 1.25x2
fx = -1(-0.375 + 0.625x + 1.25x2 + -3x3 + 0.5x3 + x4)(1 + X)(1.5 + x)

Combine like terms: -3x3 + 0.5x3 = -2.5x3
fx = -1(-0.375 + 0.625x + 1.25x2 + -2.5x3 + x4)(1 + X)(1.5 + x)

Multiply (-0.375 + 0.625x + 1.25x2 + -2.5x3 + x4) * (1 + X)
fx = -1(-0.375(1 + X) + 0.625x * (1 + X) + 1.25x2 * (1 + X) + -2.5x3 * (1 + X) + x4(1 + X))(1.5 + x)
fx = -1((1 * -0.375 + X * -0.375) + 0.625x * (1 + X) + 1.25x2 * (1 + X) + -2.5x3 * (1 + X) + x4(1 + X))(1.5 + x)
fx = -1((-0.375 + -0.375X) + 0.625x * (1 + X) + 1.25x2 * (1 + X) + -2.5x3 * (1 + X) + x4(1 + X))(1.5 + x)
fx = -1(-0.375 + -0.375X + (1 * 0.625x + X * 0.625x) + 1.25x2 * (1 + X) + -2.5x3 * (1 + X) + x4(1 + X))(1.5 + x)
fx = -1(-0.375 + -0.375X + (0.625x + 0.625xX) + 1.25x2 * (1 + X) + -2.5x3 * (1 + X) + x4(1 + X))(1.5 + x)
fx = -1(-0.375 + -0.375X + 0.625x + 0.625xX + (1 * 1.25x2 + X * 1.25x2) + -2.5x3 * (1 + X) + x4(1 + X))(1.5 + x)
fx = -1(-0.375 + -0.375X + 0.625x + 0.625xX + (1.25x2 + 1.25x2X) + -2.5x3 * (1 + X) + x4(1 + X))(1.5 + x)
fx = -1(-0.375 + -0.375X + 0.625x + 0.625xX + 1.25x2 + 1.25x2X + (1 * -2.5x3 + X * -2.5x3) + x4(1 + X))(1.5 + x)
fx = -1(-0.375 + -0.375X + 0.625x + 0.625xX + 1.25x2 + 1.25x2X + (-2.5x3 + -2.5x3X) + x4(1 + X))(1.5 + x)
fx = -1(-0.375 + -0.375X + 0.625x + 0.625xX + 1.25x2 + 1.25x2X + -2.5x3 + -2.5x3X + (1 * x4 + X * x4))(1.5 + x)
fx = -1(-0.375 + -0.375X + 0.625x + 0.625xX + 1.25x2 + 1.25x2X + -2.5x3 + -2.5x3X + (1x4 + x4X))(1.5 + x)
fx = -1(-0.375 + -0.375X + 0.625x + 0.625xX + 1.25x2 + 1.25x2X + -2.5x3 + -2.5x3X + 1x4 + x4X)(1.5 + x)

Multiply (-0.375 + -0.375X + 0.625x + 0.625xX + 1.25x2 + 1.25x2X + -2.5x3 + -2.5x3X + 1x4 + x4X) * (1.5 + x)
fx = -1(-0.375(1.5 + x) + -0.375X * (1.5 + x) + 0.625x * (1.5 + x) + 0.625xX * (1.5 + x) + 1.25x2 * (1.5 + x) + 1.25x2X * (1.5 + x) + -2.5x3 * (1.5 + x) + -2.5x3X * (1.5 + x) + 1x4 * (1.5 + x) + x4X(1.5 + x))
fx = -1((1.5 * -0.375 + x * -0.375) + -0.375X * (1.5 + x) + 0.625x * (1.5 + x) + 0.625xX * (1.5 + x) + 1.25x2 * (1.5 + x) + 1.25x2X * (1.5 + x) + -2.5x3 * (1.5 + x) + -2.5x3X * (1.5 + x) + 1x4 * (1.5 + x) + x4X(1.5 + x))
fx = -1((-0.5625 + -0.375x) + -0.375X * (1.5 + x) + 0.625x * (1.5 + x) + 0.625xX * (1.5 + x) + 1.25x2 * (1.5 + x) + 1.25x2X * (1.5 + x) + -2.5x3 * (1.5 + x) + -2.5x3X * (1.5 + x) + 1x4 * (1.5 + x) + x4X(1.5 + x))
fx = -1(-0.5625 + -0.375x + (1.5 * -0.375X + x * -0.375X) + 0.625x * (1.5 + x) + 0.625xX * (1.5 + x) + 1.25x2 * (1.5 + x) + 1.25x2X * (1.5 + x) + -2.5x3 * (1.5 + x) + -2.5x3X * (1.5 + x) + 1x4 * (1.5 + x) + x4X(1.5 + x))
fx = -1(-0.5625 + -0.375x + (-0.5625X + -0.375xX) + 0.625x * (1.5 + x) + 0.625xX * (1.5 + x) + 1.25x2 * (1.5 + x) + 1.25x2X * (1.5 + x) + -2.5x3 * (1.5 + x) + -2.5x3X * (1.5 + x) + 1x4 * (1.5 + x) + x4X(1.5 + x))
fx = -1(-0.5625 + -0.375x + -0.5625X + -0.375xX + (1.5 * 0.625x + x * 0.625x) + 0.625xX * (1.5 + x) + 1.25x2 * (1.5 + x) + 1.25x2X * (1.5 + x) + -2.5x3 * (1.5 + x) + -2.5x3X * (1.5 + x) + 1x4 * (1.5 + x) + x4X(1.5 + x))
fx = -1(-0.5625 + -0.375x + -0.5625X + -0.375xX + (0.9375x + 0.625x2) + 0.625xX * (1.5 + x) + 1.25x2 * (1.5 + x) + 1.25x2X * (1.5 + x) + -2.5x3 * (1.5 + x) + -2.5x3X * (1.5 + x) + 1x4 * (1.5 + x) + x4X(1.5 + x))
fx = -1(-0.5625 + -0.375x + -0.5625X + -0.375xX + 0.9375x + 0.625x2 + (1.5 * 0.625xX + x * 0.625xX) + 1.25x2 * (1.5 + x) + 1.25x2X * (1.5 + x) + -2.5x3 * (1.5 + x) + -2.5x3X * (1.5 + x) + 1x4 * (1.5 + x) + x4X(1.5 + x))
fx = -1(-0.5625 + -0.375x + -0.5625X + -0.375xX + 0.9375x + 0.625x2 + (0.9375xX + 0.625x2X) + 1.25x2 * (1.5 + x) + 1.25x2X * (1.5 + x) + -2.5x3 * (1.5 + x) + -2.5x3X * (1.5 + x) + 1x4 * (1.5 + x) + x4X(1.5 + x))
fx = -1(-0.5625 + -0.375x + -0.5625X + -0.375xX + 0.9375x + 0.625x2 + 0.9375xX + 0.625x2X + (1.5 * 1.25x2 + x * 1.25x2) + 1.25x2X * (1.5 + x) + -2.5x3 * (1.5 + x) + -2.5x3X * (1.5 + x) + 1x4 * (1.5 + x) + x4X(1.5 + x))
fx = -1(-0.5625 + -0.375x + -0.5625X + -0.375xX + 0.9375x + 0.625x2 + 0.9375xX + 0.625x2X + (1.875x2 + 1.25x3) + 1.25x2X * (1.5 + x) + -2.5x3 * (1.5 + x) + -2.5x3X * (1.5 + x) + 1x4 * (1.5 + x) + x4X(1.5 + x))
fx = -1(-0.5625 + -0.375x + -0.5625X + -0.375xX + 0.9375x + 0.625x2 + 0.9375xX + 0.625x2X + 1.875x2 + 1.25x3 + (1.5 * 1.25x2X + x * 1.25x2X) + -2.5x3 * (1.5 + x) + -2.5x3X * (1.5 + x) + 1x4 * (1.5 + x) + x4X(1.5 + x))
fx = -1(-0.5625 + -0.375x + -0.5625X + -0.375xX + 0.9375x + 0.625x2 + 0.9375xX + 0.625x2X + 1.875x2 + 1.25x3 + (1.875x2X + 1.25x3X) + -2.5x3 * (1.5 + x) + -2.5x3X * (1.5 + x) + 1x4 * (1.5 + x) + x4X(1.5 + x))
fx = -1(-0.5625 + -0.375x + -0.5625X + -0.375xX + 0.9375x + 0.625x2 + 0.9375xX + 0.625x2X + 1.875x2 + 1.25x3 + 1.875x2X + 1.25x3X + (1.5 * -2.5x3 + x * -2.5x3) + -2.5x3X * (1.5 + x) + 1x4 * (1.5 + x) + x4X(1.5 + x))
fx = -1(-0.5625 + -0.375x + -0.5625X + -0.375xX + 0.9375x + 0.625x2 + 0.9375xX + 0.625x2X + 1.875x2 + 1.25x3 + 1.875x2X + 1.25x3X + (-3.75x3 + -2.5x4) + -2.5x3X * (1.5 + x) + 1x4 * (1.5 + x) + x4X(1.5 + x))
fx = -1(-0.5625 + -0.375x + -0.5625X + -0.375xX + 0.9375x + 0.625x2 + 0.9375xX + 0.625x2X + 1.875x2 + 1.25x3 + 1.875x2X + 1.25x3X + -3.75x3 + -2.5x4 + (1.5 * -2.5x3X + x * -2.5x3X) + 1x4 * (1.5 + x) + x4X(1.5 + x))
fx = -1(-0.5625 + -0.375x + -0.5625X + -0.375xX + 0.9375x + 0.625x2 + 0.9375xX + 0.625x2X + 1.875x2 + 1.25x3 + 1.875x2X + 1.25x3X + -3.75x3 + -2.5x4 + (-3.75x3X + -2.5x4X) + 1x4 * (1.5 + x) + x4X(1.5 + x))
fx = -1(-0.5625 + -0.375x + -0.5625X + -0.375xX + 0.9375x + 0.625x2 + 0.9375xX + 0.625x2X + 1.875x2 + 1.25x3 + 1.875x2X + 1.25x3X + -3.75x3 + -2.5x4 + -3.75x3X + -2.5x4X + (1.5 * 1x4 + x * 1x4) + x4X(1.5 + x))
fx = -1(-0.5625 + -0.375x + -0.5625X + -0.375xX + 0.9375x + 0.625x2 + 0.9375xX + 0.625x2X + 1.875x2 + 1.25x3 + 1.875x2X + 1.25x3X + -3.75x3 + -2.5x4 + -3.75x3X + -2.5x4X + (1.5x4 + 1x5) + x4X(1.5 + x))
fx = -1(-0.5625 + -0.375x + -0.5625X + -0.375xX + 0.9375x + 0.625x2 + 0.9375xX + 0.625x2X + 1.875x2 + 1.25x3 + 1.875x2X + 1.25x3X + -3.75x3 + -2.5x4 + -3.75x3X + -2.5x4X + 1.5x4 + 1x5 + (1.5 * x4X + x * x4X))
fx = -1(-0.5625 + -0.375x + -0.5625X + -0.375xX + 0.9375x + 0.625x2 + 0.9375xX + 0.625x2X + 1.875x2 + 1.25x3 + 1.875x2X + 1.25x3X + -3.75x3 + -2.5x4 + -3.75x3X + -2.5x4X + 1.5x4 + 1x5 + (1.5x4X + x5X))

Reorder the terms:
fx = -1(-0.5625 + -0.5625X + -0.375x + 0.9375x + -0.375xX + 0.9375xX + 0.625x2 + 1.875x2 + 0.625x2X + 1.875x2X + 1.25x3 + -3.75x3 + 1.25x3X + -3.75x3X + -2.5x4 + 1.5x4 + -2.5x4X + 1.5x4X + 1x5 + x5X)

Combine like terms: -0.375x + 0.9375x = 0.5625x
fx = -1(-0.5625 + -0.5625X + 0.5625x + -0.375xX + 0.9375xX + 0.625x2 + 1.875x2 + 0.625x2X + 1.875x2X + 1.25x3 + -3.75x3 + 1.25x3X + -3.75x3X + -2.5x4 + 1.5x4 + -2.5x4X + 1.5x4X + 1x5 + x5X)

Combine like terms: -0.375xX + 0.9375xX = 0.5625xX
fx = -1(-0.5625 + -0.5625X + 0.5625x + 0.5625xX + 0.625x2 + 1.875x2 + 0.625x2X + 1.875x2X + 1.25x3 + -3.75x3 + 1.25x3X + -3.75x3X + -2.5x4 + 1.5x4 + -2.5x4X + 1.5x4X + 1x5 + x5X)

Combine like terms: 0.625x2 + 1.875x2 = 2.5x2
fx = -1(-0.5625 + -0.5625X + 0.5625x + 0.5625xX + 2.5x2 + 0.625x2X + 1.875x2X + 1.25x3 + -3.75x3 + 1.25x3X + -3.75x3X + -2.5x4 + 1.5x4 + -2.5x4X + 1.5x4X + 1x5 + x5X)

Combine like terms: 0.625x2X + 1.875x2X = 2.5x2X
fx = -1(-0.5625 + -0.5625X + 0.5625x + 0.5625xX + 2.5x2 + 2.5x2X + 1.25x3 + -3.75x3 + 1.25x3X + -3.75x3X + -2.5x4 + 1.5x4 + -2.5x4X + 1.5x4X + 1x5 + x5X)

Combine like terms: 1.25x3 + -3.75x3 = -2.5x3
fx = -1(-0.5625 + -0.5625X + 0.5625x + 0.5625xX + 2.5x2 + 2.5x2X + -2.5x3 + 1.25x3X + -3.75x3X + -2.5x4 + 1.5x4 + -2.5x4X + 1.5x4X + 1x5 + x5X)

Combine like terms: 1.25x3X + -3.75x3X = -2.5x3X
fx = -1(-0.5625 + -0.5625X + 0.5625x + 0.5625xX + 2.5x2 + 2.5x2X + -2.5x3 + -2.5x3X + -2.5x4 + 1.5x4 + -2.5x4X + 1.5x4X + 1x5 + x5X)

Combine like terms: -2.5x4 + 1.5x4 = -1x4
fx = -1(-0.5625 + -0.5625X + 0.5625x + 0.5625xX + 2.5x2 + 2.5x2X + -2.5x3 + -2.5x3X + -1x4 + -2.5x4X + 1.5x4X + 1x5 + x5X)

Combine like terms: -2.5x4X + 1.5x4X = -1x4X
fx = -1(-0.5625 + -0.5625X + 0.5625x + 0.5625xX + 2.5x2 + 2.5x2X + -2.5x3 + -2.5x3X + -1x4 + -1x4X + 1x5 + x5X)
fx = (-0.5625 * -1 + -0.5625X * -1 + 0.5625x * -1 + 0.5625xX * -1 + 2.5x2 * -1 + 2.5x2X * -1 + -2.5x3 * -1 + -2.5x3X * -1 + -1x4 * -1 + -1x4X * -1 + 1x5 * -1 + x5X * -1)
fx = (0.5625 + 0.5625X + -0.5625x + -0.5625xX + -2.5x2 + -2.5x2X + 2.5x3 + 2.5x3X + 1x4 + 1x4X + -1x5 + -1x5X)

Solving
fx = 0.5625 + 0.5625X + -0.5625x + -0.5625xX + -2.5x2 + -2.5x2X + 2.5x3 + 2.5x3X + 1x4 + 1x4X + -1x5 + -1x5X

Solving for variable 'f'.

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

Divide each side by 'x'.
f = 0.5625x-1 + 0.5625x-1X + -0.5625 + -0.5625X + -2.5x + -2.5xX + 2.5x2 + 2.5x2X + x3 + x3X + -1x4 + -1x4X

Simplifying
f = 0.5625x-1 + 0.5625x-1X + -0.5625 + -0.5625X + -2.5x + -2.5xX + 2.5x2 + 2.5x2X + x3 + x3X + -1x4 + -1x4X

Reorder the terms:
f = -0.5625 + -0.5625X + 0.5625x-1 + 0.5625x-1X + -2.5x + -2.5xX + 2.5x2 + 2.5x2X + x3 + x3X + -1x4 + -1x4X

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