10x^2+19x-15=0

Solve for x over the real numbers using factor method:
10 x^2 + 19 x - 15 = 0

The left hand side factors into a product with two terms:
(2 x + 5) (5 x - 3) = 0

Split into two equations:
2 x + 5 = 0 or 5 x - 3 = 0

Subtract 5 from both sides:
2 x = -5 or 5 x - 3 = 0

Divide both sides by 2:
x = -5/2 or 5 x - 3 = 0

Add 3 to both sides:
x = -5/2 or 5 x = 3

Divide both sides by 5:

  x = -5/2 or x = 3/5