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.

17 is not an equation.

19. What terms give a product of -3 and add 5 of one and one of the other to give -2?

20. Is there a typo in this question?

I hope this helps. Thanks for asking.

Sure! I'll help you solve these three equations and explain the steps involved in solving them.

17. Solve the equation using the zero product property:
To use the zero product property, we set each factor equal to zero and solve for the variable.

-8n(5n+3) = 0

To solve for n, we can set each factor equal to zero and solve them separately:
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 solutions to the equation are n = 0 and n = -3/5.

19. Solve the equation by factoring:
To solve an equation by factoring, we need to rewrite it as a product of factors set equal to zero.

5z^2 - 2z - 3 = 0

First, check if the equation can be factored further. In this case, it can be factored using the method of grouping.

Split the middle term -2z into two terms such that their sum is -2z, and their product is -15z^2:
5z^2 - 5z + 3z - 3 = 0

Factor the equation by grouping:
(5z^2 - 5z) + (3z - 3) = 0
5z(z - 1) + 3(z - 1) = 0
(z - 1)(5z + 3) = 0

To find the solutions, we set each factor equal to zero:
First factor: z - 1 = 0
z = 1

Second factor: 5z + 3 = 0
5z = -3
z = -3/5

Thus, the solutions to the equation are z = 1 and z = -3/5.

20. Solve the equation by completing the square:
To solve an equation by completing the square, we make one side of the equation a perfect square trinomial and then solve for the variable.

x^2 - 3x = 4

Move the constant term to the right side of the equation:
x^2 - 3x - 4 = 0

To complete the square, we need to add and subtract the square of half the coefficient of the x-term. In this case, the coefficient is -3, so we take half of it (-3/2) and square it (9/4):

x^2 - 3x + 9/4 - 9/4 - 4 = 0

Rearrange the terms:
(x^2 - 3x + 9/4) - 25/4 = 0

Simplify:
(x - 3/2)^2 - 25/4 = 0

Add 25/4 to both sides:
(x - 3/2)^2 = 25/4

Take the square root of both sides:
x - 3/2 = ± √(25/4)

Simplify:
x - 3/2 = ± 5/2

Now, solve for x:
First case: x - 3/2 = 5/2
x = 5/2 + 3/2
x = 8/2
x = 4

Second case: x - 3/2 = -5/2
x = -5/2 + 3/2
x = -2/2
x = -1

Therefore, the solutions to the equation are x = 4 and x = -1.

I hope these explanations help you understand how to solve these types of problems. If you have any further questions, feel free to ask!