How do I solve -3p^2+66p=0

Have you been talking about factoring in class? We can solve it that way.

I have learned factoring but I do not know what to do for this problem

That's all right. Begin by factoring out what is common to all terms. Here is an example...

9x^2 - 81x = 0

In this problem, all terms have an x in them and all terms are divisible by 9. The common term is "9x," so factor that out.

9x(x - 9) = 0

If you want to check, just distribute the 9x in, and we get our original.

Now set each term equal to 0.

9x = 0, x - 9 = 0
x = 0, x = 9
Those are our answers.

What do you come up with for your problem?

I got 3p(-p^2+22)

Now what

That's close, but you forgot to factor the p out of -3p^2. You should have

3p(-p+22) = 0

Then, set each term equal to 0.

To solve the equation -3p^2 + 66p = 0, you need to find the values of the variable p that make the equation true. Here's how you can do it step by step:

Step 1: Factor out the common factor, if possible.
In this equation, both terms have a common factor of p. Taking out p as a common factor, we get:
p(-3p + 66) = 0

Step 2: Set each factor equal to zero.
Since a product of factors is zero if and only if at least one of the factors is zero, we set each factor equal to zero and solve for p:
p = 0
-3p + 66 = 0

Step 3: Solve for p in the second equation.
To solve -3p + 66 = 0, we isolate the p term by subtracting 66 from both sides of the equation:
-3p = -66
Divide both sides by -3 to solve for p:
p = -66 / -3
p = 22

Step 4: Check the solutions.
To check if the solutions are correct, substitute each value of p back into the original equation and see if it holds true.
When p = 0:
-3(0)^2 + 66(0) = 0
0 = 0 (True)

When p = 22:
-3(22)^2 + 66(22) = 0
-1452 + 1452 = 0
0 = 0 (True)

Therefore, the solutions to the equation -3p^2 + 66p = 0 are p = 0 and p = 22.