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.

you find the 2 factors of -3 sum of which wiil give you -4

Sure! I'd be happy to help you with these three problems and guide you through the process of solving them. Let's start with problem number 17.

17. Solve the equation using the zero product property:

The zero product property states that if the product of two factors equals zero, then at least one of the factors must be zero.

-8n(5n+3) = 0

To solve this equation, we set each of the factors equal to zero and solve for n.

First factor:
-8n = 0
Divide both sides by -8:
n = 0

Second factor:
5n + 3 = 0
Subtract 3 from both sides:
5n = -3
Divide both sides by 5:
n = -3/5

Therefore, the solution to the equation -8n(5n+3) = 0 is n = 0 and n = -3/5.

Now let's move on to problem number 19.

19. Solve the equation by factoring:

5z^2 - 2z - 3 = 0

To solve this equation by factoring, we need to find two numbers that multiply to give the product of the coefficient of z^2 (5) and the constant term (-3), and add up to give the coefficient of z (-2).

The factors of 5 are 1 and 5, and they can be negative as well. The factors of -3 are -1 and 3, and again, they can be negative.

Let's try the combinations and see if we can find the correct factors:

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

Now we can use the zero product property to set each factor equal to zero and solve for z.

First factor:
5z - 3 = 0
Add 3 to both sides:
5z = 3
Divide both sides by 5:
z = 3/5

Second factor:
z + 1 = 0
Subtract 1 from both sides:
z = -1

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

Finally, let's move on to problem number 20.

20. Solve the equation by completing the square:

x^2 - 3x = 4

To solve this equation by completing the square, we need to add a constant term on both sides of the equation to make it a perfect square trinomial.

First, let's take half of the coefficient of x (-3/2) and square it to get (-3/2)^2 = 9/4.

Add this constant term (9/4) on both sides of the equation:

x^2 - 3x + 9/4 = 4 + 9/4
x^2 - 3x + 9/4 = 25/4

Now, we can factor the left side as a perfect square trinomial:

(x - 3/2)^2 = 25/4

Taking the square root of both sides:

x - 3/2 = ±(√(25/4))
x - 3/2 = ±(5/2)

Now we can solve for x by adding 3/2 to both sides:

x = 3/2 ± 5/2

x = (3 ± 5)/2

Therefore, the solution to the equation x^2 - 3x = 4 is x = (3 + 5)/2 and x = (3 - 5)/2, which simplifies to x = 4 and x = -1/2.

I hope this explanation helps you understand how to solve these types of problems. Let me know if you have any further questions!