f(x)=(3x-2)(x^2-4x+5)

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Solution for f(x)=(3x-2)(x^2-4x+5) equation: 


Simplifying
f(x) = (3x + -2)(x2 + -4x + 5)

Multiply f * x
fx = (3x + -2)(x2 + -4x + 5)

Reorder the terms:
fx = (-2 + 3x)(x2 + -4x + 5)

Reorder the terms:
fx = (-2 + 3x)(5 + -4x + x2)

Multiply (-2 + 3x) * (5 + -4x + x2)
fx = (-2(5 + -4x + x2) + 3x * (5 + -4x + x2))
fx = ((5 * -2 + -4x * -2 + x2 * -2) + 3x * (5 + -4x + x2))
fx = ((-10 + 8x + -2x2) + 3x * (5 + -4x + x2))
fx = (-10 + 8x + -2x2 + (5 * 3x + -4x * 3x + x2 * 3x))
fx = (-10 + 8x + -2x2 + (15x + -12x2 + 3x3))

Reorder the terms:
fx = (-10 + 8x + 15x + -2x2 + -12x2 + 3x3)

Combine like terms: 8x + 15x = 23x
fx = (-10 + 23x + -2x2 + -12x2 + 3x3)

Combine like terms: -2x2 + -12x2 = -14x2
fx = (-10 + 23x + -14x2 + 3x3)

Solving
fx = -10 + 23x + -14x2 + 3x3

Solving for variable 'f'.

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

Divide each side by 'x'.
f = -10x-1 + 23 + -14x + 3x2

Simplifying
f = -10x-1 + 23 + -14x + 3x2

Reorder the terms:
f = 23 + -10x-1 + -14x + 3x2

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