Answer: [tex]x=\frac{3}{5} , -1[/tex]
Step-by-step explanation:
To solve this equation, we must first factor it. By multiplying the lead coefficient and the constant, we are looking for two numbers that multiply to -15. By looking at the middle term, we can also tell that we are looking for two numbers that add to 2. These numbers are 5 and -3. So, we must split the middle term into 5x and -3x, and group our equation by the first two terms and the last two terms. Now, our equation looks like this:
[tex](5x^2 + 5x)+(-3x-3) = 0[/tex]
Now, we must factor out the GCF (greatest common factor) out of both of these groups. Now, our equation looks like this:
[tex]5x(x+1)-3(x+1) = 0[/tex]
Since (x+1) is a factor of both of these terms, we can factor this out, and we are left with:
[tex](5x-3)(x+1)=0[/tex]
Now, using the Zero Product Property, we can separately set each term equal to zero in order to find the solutions.
- When 5x - 3 = 0, x = 3/5.
- When x + 1 = 0, x = -1
