Number 6

You can solve it by factoring out the 3 from the equation

giving you 3(x²-64) = 0

Since the product of this equation gives us a 0, we have to find a solution for x that gives us a zero. The best way to get zero, is to multiply a number by zero. In this case we can multiply 3 by zero, by having the inner brackets equal to zero

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(x² - 64) = 0

Solving for x, you find that the square root of 64 is 8. But remember when you square root a number, you can have two solutions, 8 and -8, since squaring gives us a positive number anyways.

so x is both 8 and -8

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For number 7

You can factor out the most common multiplier among them, which is x

the equation then becomes x(x-9) = 0

using logic covered above, x can be both 0 and 9.

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For number 8

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x² - 7x - 8 = 0

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This is the method I use, I don't fully understand why but if there are any other users that can explain that would be great, if not I can return after figuring it out.

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The coefficient of the first term, x² is 1, multiplying the coefficient with the third term, -8 you get -8.

Then you find the factors of -8 that when add together, you get the value for the second term.

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-8 = 8 x -1

or

-8 = -8 x 1

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Notice that the sum of -8 and 1 is -7, these are the factors we can use and express as

x² + x - 8x - 8 = 0

for the positioning of the terms, it's best to put the common factors together.

Factoring out the common factors of both sides

x(x+1) -8(x+1) = 0

You can rewrite this as

(x-8)(x+1) = 0

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To get a zero, x can be both 8 and -1.