f(x)=0.5x(x^2+8x+16)(2x-3)

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Solution for f(x)=0.5x(x^2+8x+16)(2x-3) equation:


Simplifying
f(x) = 0.5x(x2 + 8x + 16)(2x + -3)

Multiply f * x
fx = 0.5x(x2 + 8x + 16)(2x + -3)

Reorder the terms:
fx = 0.5x(16 + 8x + x2)(2x + -3)

Reorder the terms:
fx = 0.5x(16 + 8x + x2)(-3 + 2x)

Multiply (16 + 8x + x2) * (-3 + 2x)
fx = 0.5x(16(-3 + 2x) + 8x * (-3 + 2x) + x2(-3 + 2x))
fx = 0.5x((-3 * 16 + 2x * 16) + 8x * (-3 + 2x) + x2(-3 + 2x))
fx = 0.5x((-48 + 32x) + 8x * (-3 + 2x) + x2(-3 + 2x))
fx = 0.5x(-48 + 32x + (-3 * 8x + 2x * 8x) + x2(-3 + 2x))
fx = 0.5x(-48 + 32x + (-24x + 16x2) + x2(-3 + 2x))
fx = 0.5x(-48 + 32x + -24x + 16x2 + (-3 * x2 + 2x * x2))
fx = 0.5x(-48 + 32x + -24x + 16x2 + (-3x2 + 2x3))

Combine like terms: 32x + -24x = 8x
fx = 0.5x(-48 + 8x + 16x2 + -3x2 + 2x3)

Combine like terms: 16x2 + -3x2 = 13x2
fx = 0.5x(-48 + 8x + 13x2 + 2x3)
fx = (-48 * 0.5x + 8x * 0.5x + 13x2 * 0.5x + 2x3 * 0.5x)
fx = (-24x + 4x2 + 6.5x3 + 1x4)

Solving
fx = -24x + 4x2 + 6.5x3 + 1x4

Solving for variable 'f'.

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

Divide each side by 'x'.
f = -24 + 4x + 6.5x2 + x3

Simplifying
f = -24 + 4x + 6.5x2 + x3

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