Question

`5x^2+5x-30=0`

Please Include Work

Answer 1

`x=2,-3`

Explanation:

`5x^2+5x-30=0`

To factor, see which number fits into each of the terms. In this case, factor out 5:

`5(x^2+x-6)=0`

Now factor
`x^2+x-6`. You need to find two numbers whose sums will add up to 1 (because 1x) and whose product will be -6. Since the product is negative, we will need to use a positive and a negative number:

`-2,3\\-2+3=1\\-2*3=-6`

Rewrite the equation using the above values:

`(x-2)(x+3)\\\\5(x-2)(x+3)=0`

Since the left side must equal zero, we can conclude that one of the terms on the left side is equal to zero. It can be either one or both. Separate the parentheses and set them to zero, the solve each for x:

`x-2=0\\x-2+2=0+2\\x=2\\\\x+3=0\\x+3-3=0-3\\x=-3`

So;

`x=2,-3`