f(x)=(x-5)(x+6)(x-10)

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Solution for f(x)=(x-5)(x+6)(x-10) equation: 


Simplifying
f(x) = (x + -5)(x + 6)(x + -10)

Multiply f * x
fx = (x + -5)(x + 6)(x + -10)

Reorder the terms:
fx = (-5 + x)(x + 6)(x + -10)

Reorder the terms:
fx = (-5 + x)(6 + x)(x + -10)

Reorder the terms:
fx = (-5 + x)(6 + x)(-10 + x)

Multiply (-5 + x) * (6 + x)
fx = (-5(6 + x) + x(6 + x))(-10 + x)
fx = ((6 * -5 + x * -5) + x(6 + x))(-10 + x)
fx = ((-30 + -5x) + x(6 + x))(-10 + x)
fx = (-30 + -5x + (6 * x + x * x))(-10 + x)
fx = (-30 + -5x + (6x + x2))(-10 + x)

Combine like terms: -5x + 6x = 1x
fx = (-30 + 1x + x2)(-10 + x)

Multiply (-30 + 1x + x2) * (-10 + x)
fx = (-30(-10 + x) + 1x * (-10 + x) + x2(-10 + x))
fx = ((-10 * -30 + x * -30) + 1x * (-10 + x) + x2(-10 + x))
fx = ((300 + -30x) + 1x * (-10 + x) + x2(-10 + x))
fx = (300 + -30x + (-10 * 1x + x * 1x) + x2(-10 + x))
fx = (300 + -30x + (-10x + 1x2) + x2(-10 + x))
fx = (300 + -30x + -10x + 1x2 + (-10 * x2 + x * x2))
fx = (300 + -30x + -10x + 1x2 + (-10x2 + x3))

Combine like terms: -30x + -10x = -40x
fx = (300 + -40x + 1x2 + -10x2 + x3)

Combine like terms: 1x2 + -10x2 = -9x2
fx = (300 + -40x + -9x2 + x3)

Solving
fx = 300 + -40x + -9x2 + x3

Solving for variable 'f'.

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

Divide each side by 'x'.
f = 300x-1 + -40 + -9x + x2

Simplifying
f = 300x-1 + -40 + -9x + x2

Reorder the terms:
f = -40 + 300x-1 + -9x + x2

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