Algebra factoring ax²+bx+c

1.) 2x²-3x-5=0

2.) 6x²-17x+5=0

3.) 28y²-y-15=0

For factoring in algebra, you usually see if you can get some factors of the a and of the c to FOIL (first, outside, inside, last = order of multiplication in the parenthesis) it out. If this doesn't work, then you refer to the quadratic formula, which is (-b + [or] - [radical] ((b^2) - 4ac))/2a.
1) You can factor this one out to be (2x - 5)(x + 1) = 0. If need be, you can solve for x by making both (2x + 5) and (x + 1) equal to zero (Your answers would be -5/2 and - 1).
2) You can factor this one out to be (2x - 5)(3x - 1) = 0 (x = 5/2 and 1/3).
3) You can factor this one out to be (7x + 5)(4x - 3) = 0 (x = -5/7 and 3/4).

1) 2x^2 -3x - 5 ; Find 2 numbers m and n such that m+n = b and mn = ac (consider the signs)
here m+n = -3 and mn = - 10. The numbers are 2 and -5
The expr = 2x^2 + 2x - 5x - 5 = 2x(x +2) - 5(x + 2)(2x -5)
2) m+n = - 17 and mn = 30. The numbers are -15 and -2
The expr = 6x^2 - 15x - 2x + 5 = 3x(2x - 5) - (2x - 5) = (2x -5)(3x - 1)
3) m+n = -1 and mn = - 420. The numbers are 20 and - 21
The expr = 28y^2 + 20y - 21y - 15 = 4y(7y + 5) - 3(7y + 5) = (7y + 5)(4y - 3)

use the formula

(-b (+/-) sqrt ((b^2)-4ac) / 2a

1) (2x-5)(x+1)=0
2) (2x-5)(3x-1)=0
3) (4y-3)(7y+5)=0