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.

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

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.

Of course! I'd be happy to help you with these three problems and explain the steps involved in solving them.

17. To solve the equation -8n(5n+3) = 0 using the zero product property, we set each term equal to zero and solve for n.

First, we set -8n = 0:
-8n = 0
Divide both sides by -8:
n = 0

Then, we set 5n+3 = 0:
5n+3 = 0
Subtract 3 from both sides:
5n = -3
Divide both sides by 5:
n = -3/5

So, the solutions to the equation -8n(5n+3) = 0 are n = 0 and n = -3/5.

19. To solve the equation 5z^2-2z-3 = 0 by factoring, we need to find two binomials that multiply together to give us the original quadratic equation.

First, we break the middle term (-2z) into two terms such that their product is equal to the product of the coefficient of the quadratic term (5) and the constant term (-3). In this case, we can rewrite -2z as -5z+3z.

Now, we have the equation:
5z^2 - 5z + 3z - 3 = 0

We group the terms:
(5z^2 - 5z) + (3z - 3) = 0

Factor out the common terms from each group:
5z(z - 1) + 3(z - 1) = 0

Now, notice that we have a common binomial factor of (z - 1) in both terms. We can factor it out:
(z - 1)(5z + 3) = 0

Using the zero product property, we set each factor equal to zero and solve for z:
z - 1 = 0
z = 1

5z + 3 = 0
5z = -3
z = -3/5

Therefore, the solutions to the equation 5z^2-2z-3 = 0 are z = 1 and z = -3/5.

20. To solve the equation x^2 - 3x = 4 by completing the square, we need to rewrite the quadratic expression in a perfect square form.

First, we move the constant term (4) to the right side of the equation:
x^2 - 3x - 4 = 0

Then, we "complete the square" by taking half of the coefficient of the x-term (-3/2), squaring it ((-3/2)^2 = 9/4), and adding it to both sides of the equation:
x^2 - 3x + 9/4 - 4 - 9/4 = 0
(x - 3/2)^2 - 25/4 = 0

Now, we simplify the equation:
(x - 3/2)^2 - 25/4 = 0

To solve for x, we take the square root of both sides:
sqrt((x - 3/2)^2) - sqrt(25/4) = 0

(x - 3/2) - 5/2 = 0 or (x - 3/2) + 5/2 = 0

Simplifying further, we get:
x - 3/2 - 5/2 = 0 or x - 3/2 + 5/2 = 0

x - 4 = 0 or x + 1 = 0

Solving for x in each equation gives us:
x = 4 or x = -1

Therefore, the solutions to the equation x^2 - 3x = 4 by completing the square are x = 4 and x = -1.

I hope this helps! Let me know if you have any further questions.