SOLUTION: For the function f(x) = x³ + 3x² – 70x – 144, f(–9) = 0, f(–2) = 0, and f(8) = 0. What are the solutions to the equation x³ + 3x² = 70x

This is a giveaway problem to anyone who understands it.
I'll go through it to show why it is a giveaway problem:

f(x) = x3 + 3x2 – 70x – 144

f(–9) = 0

That tells us that if you plug in (-9) for x in

f(x) = x3 + 3x2 – 70x – 144, we get 0

That means that -9 is a solution to 

f(x) = x3 + 3x2 – 70x – 144 = 0

Checking to make sure that he has told us the truth:
[Not necessary if we trust the problem-maker :) ]

f(-9) = (-9)3 + 3(-9)2 – 70(-9) – 144
f(-9) = -729 + 3(81) + 630 - 144
f(-9) = -729 + 243 + 630 - 144
f(-9) = 0  

The problem-maker told us the truth! f(-9) = 0.
So we'll trust him to have told us the truth on the others.

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f(–2) = 0

That tells us that if we plug in (-2) for x in

f(x) = x3 + 3x2 – 70x – 144, we get 0, that is:

That means that -2 is a solution to 

f(x) = x3 + 3x2 – 70x – 144 = 0

We'll trust him that the above does give 0

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f(8) = 0

That tells us that if we plug in (8) for x in

f(x) = x3 + 3x2 – 70x – 144, we get 0, that is:

That means that 8 is a solution to 

f(x) = x3 + 3x2 – 70x – 144 = 0

We'll trust him that the above does give 0

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So the solutions are –9, –2, and 8

Because telling us that f(–9) = 0, f(–2) = 0, and f(8) = 0, tells
us the solutions, what values we must plug into f(x) to get 0, and since 
f(x) equals to x3 + 3x2 – 70x – 144, those values in the parentheses
are what values we must plug into x3 + 3x2 – 70x – 144 to get 0.
So they have to be solutions to the equationn x3 + 3x2 – 70x – 144 = 0.
See why it's a giveaway problem? -- like "Who's buried in Grant's tomb?" :)

Edwin