Question

Solve the quadratic equation by factoring: 15x^2+4x-4=0

Answer 1

We can factor by grouping. To do so, we multiply the leading coefficient with the constant at the end. In other words, a times c (ax^2 + bx + c).

15*-4 = -60

Now we need to split the b term into two pieces that multiply to -60 and add to 4.

-6 and 10 will work.

Now group one part of b with the 15x^2 and the other part with -4.

(15x^2 + 10x) + (-6x - 4)

Now factor both terms.

5x(3x+2) - 2(3x+2)

3x+2 is one of our factors and 5x-2 is the other.

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

Now just find the zeros.

3x+2 = 0
3x = -2
x = -2/3

And

5x-2 = 0
5x = 2
x = 2/5

So the answer is x = -2/3 and x = 2/5