Question

Solve by applying the zero product property.

8m(m+3)=2m-15

Find the solution set.

Answer 1

You'll need to get just a zero on one side.

Answer 2

@tkhunny Could you please explain how, or give me an example?

Answer 3

Ever see one of these? \(ax^{2} + bx + c = 0\) It's a quadratic equation. It MUST have zero alone, by itself, on one side. You do this by addition and subtraction.

8m(m+3) = 2m - 15

Subtract 2m from each side

8m(m+3) - 2m = 2m - 15 - 2m

8m(m+3) - 2m = 2m - 2m - 15

8m(m+3) - 2m = 0 - 15

8m(m+3) - 2m = - 15

You may wish to expand the left hand side using the distributive property.

8m^2 + 24m - 2m = - 15

Sweet. Some "like" terms we can combine.

8m^2 + 22m = - 15

Okay, now you take care of the -15.

Answer 4

Is this right?
\[8m^2+22m+15\]

Answer 5

@tkhunny

Answer 6

@NekoAisu

Yes, if you write = 0 at the end. This is an equation.

8 m ^2 + 22 m +15 = 0

Answer 7

@Directrix Thank you, but what do I need to do now? I need to find the solution set. Do I try to factor it?

Answer 8

Yes.

Factor this:

8 m ^2 + 22 m +15 = 0

Answer 9

(4m + 5) * ( ? + ?) = 0

I did one factor. You do the other, okay?

Answer 10

(2m+3)?
@Directrix

Answer 11

(4m + 5) * ( 2m + 3) = 0

Zero Product Property

4m + 5 = 0 OR 2m + 3 = 0

Solve each of those separately for m.

Answer 12

m = -5/4 or m = -3/2?
@Directrix

Answer 13

Correct.

Answer 14

@Directrix Thank You!

Answer 15

You are welcome.