f(x)=x(x+4)(x-6)(x+7)

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Solution for f(x)=x(x+4)(x-6)(x+7) equation:


Simplifying
f(x) = x(x + 4)(x + -6)(x + 7)

Multiply f * x
fx = x(x + 4)(x + -6)(x + 7)

Reorder the terms:
fx = x(4 + x)(x + -6)(x + 7)

Reorder the terms:
fx = x(4 + x)(-6 + x)(x + 7)

Reorder the terms:
fx = x(4 + x)(-6 + x)(7 + x)

Multiply (4 + x) * (-6 + x)
fx = x(4(-6 + x) + x(-6 + x))(7 + x)
fx = x((-6 * 4 + x * 4) + x(-6 + x))(7 + x)
fx = x((-24 + 4x) + x(-6 + x))(7 + x)
fx = x(-24 + 4x + (-6 * x + x * x))(7 + x)
fx = x(-24 + 4x + (-6x + x2))(7 + x)

Combine like terms: 4x + -6x = -2x
fx = x(-24 + -2x + x2)(7 + x)

Multiply (-24 + -2x + x2) * (7 + x)
fx = x(-24(7 + x) + -2x * (7 + x) + x2(7 + x))
fx = x((7 * -24 + x * -24) + -2x * (7 + x) + x2(7 + x))
fx = x((-168 + -24x) + -2x * (7 + x) + x2(7 + x))
fx = x(-168 + -24x + (7 * -2x + x * -2x) + x2(7 + x))
fx = x(-168 + -24x + (-14x + -2x2) + x2(7 + x))
fx = x(-168 + -24x + -14x + -2x2 + (7 * x2 + x * x2))
fx = x(-168 + -24x + -14x + -2x2 + (7x2 + x3))

Combine like terms: -24x + -14x = -38x
fx = x(-168 + -38x + -2x2 + 7x2 + x3)

Combine like terms: -2x2 + 7x2 = 5x2
fx = x(-168 + -38x + 5x2 + x3)
fx = (-168 * x + -38x * x + 5x2 * x + x3 * x)
fx = (-168x + -38x2 + 5x3 + x4)

Solving
fx = -168x + -38x2 + 5x3 + 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 = -168 + -38x + 5x2 + x3

Simplifying
f = -168 + -38x + 5x2 + x3

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