Solve the equation: (3x - 2)(7x + 1) = 0.

Question

callisto · Answer

(3x - 2)(7x + 1) = 0
Put (3x - 2) =0 or  (7x + 1) = 0
            x = 2/3              x=-1/7
actually do you understand how to deal with such kind of questions?

anonymous · Answer

I don;t :(

callisto · Answer

Give you an easy one to try
x (5) = 0, what is x?

anonymous · Answer

attachment

callisto · Answer

How can you get the answer?

anonymous · Answer

Multiplying something by zero always results in a zero.

callisto · Answer

Yup.. that's the same when you consider the xy=0
What would you think if xy=0?
what is the possible value for x or y?

callisto · Answer

Hint: remember what you've said just now 'Multiplying something by zero always results in a zero.'

anonymous · Answer

I'm not exactly sure how to work the double letters unfortunately. I know if you multiple one by zero it gets zero? I think.

callisto · Answer

Yup.. you're quite close to the point.. For the product of 2 unknowns, the either one should be =0 to give 0 as the result (of course both of them can be 0), Do you understand so far?

anonymous · Answer

Yeah, I understand so far. Until numbers get added into the situation which makes it twice as difficult.

callisto · Answer

When you see something like (3x - 2)(7x + 1) = 0.
Just consider (3x - 2) =y and (7x + 1)=z
So yz=0
Understand so far?

anonymous · Answer

Sort of.

callisto · Answer

So, either y = 0 or z=0 can make the product =0, understand?

anonymous · Answer

Now it makes more sense.

callisto · Answer

So remember you let y=(3x - 2) and z=(7x + 1) 
Put it back to y = 0 or z=0 respectively, and solve for it separately, understand?

anonymous · Answer

That part kind of confuses me the final solve.

callisto · Answer

Hmmm... which part you don't understand?

anonymous · Answer

So remember you let y=(3x - 2) and z=(7x + 1) Put it back to y = 0 or z=0 respectively, and solve for it separately, understand?

callisto · Answer

So remember you let y=(3x - 2) and z=(7x + 1) <- understand?

anonymous · Answer

Yes I understand that part.

callisto · Answer

either y = 0 or z=0 can make the product =0, understand <- understand?

anonymous · Answer

That's where I get confused.

callisto · Answer

yz=0
either y = 0 or z=0 can make the product =0, understand?

anonymous · Answer

Yeah

callisto · Answer

so y= 3x-2 =0 or z=7x+1=0, understand?

anonymous · Answer

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callisto · Answer

So 3x-2 =0 or 7x+1=0
and solve the 2 equations, understand?

anonymous · Answer

I don't know how to solve them both together.

callisto · Answer

3x-2 =0
x = 2/3
or
7x+1 =0
x=-1/7
Just solve it separately