# Math

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I need help with these three problems. They are on a Study Guide and I need some refreshing up of how to do them.

17. Solve the equation using the zero product property...

-8n(5n+3)

19. Solve the equation by factoring

5z^2-2z-3=0

20. Solve the equation by completing the square..

x^-3x=4

Thank you.. Please show me how you did it if possible.

• Math -

in #1 you probably meant
-8n(5n+3) = 0

When you have the product of two or more factors equal to zero and the result is zero, that can only happen if any one of the factors equal to zero.
so-8n = 0, then n = 0
or
5n+3 = 0,
5n=-3
n=-3/5

#2
5z^2-2z-3=0
(5z + 3)(z - 1) = 0
then 5z+3 = 0 or z-1 = 0
z = -3/5 or z=1

#3 did you mean
x^2-3x=4 ?

take 1/2 of the middle term coefficient, square it, then add to both sides
1/2 of -3 is -3/2, square that gives you 9/4

x^2 - 3x + 9/4 = 4 + 9/4
(x-3/2)^2 = 25/4
x - 3/2 = +- 5/2
x = 3/2 +- 5/2
x = 4 or -1

• Math -

in my solution to #2
the (5z + 3)(z - 1) = 0
should have been

(5z - 3)(z + 1) = 0

Please make the necessary corrections in my solution, sorry about the slip.

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