Given:
(y+2)(y-5)=2y+2
Use the F.O.I.L method to multiply the left hand side:
y² - 5y + 2y -10 = 2y + 2
Subtract 2y + 2 from both sides:
y² - 5y - 12 = 0
You know have a quadratic of the form ay² + by + c = 0
Check that it has real roots by evaluating the discriminate, b² - 4(a)(c):
(-5)² - 4(1)(-12) = 25 + 48 = 73
It is greater than zero so you have two real roots:
Use the quadratic formula to find the two roots:
x = (-b + sqrt(b² - 4(a)(c))}/2a
x = (-b - sqrt(b² - 4(a)(c))}/2a