To solve the equation, we need to find a common denominator for the fractions on both sides. The least common denominator (LCD) for 6, 25, and 15 is 150.

Multiplying both sides of the equation by 150, we get:

150(X - 4/6) = 150(5/25) + 150(-7/15)

Simplifying:

150X - 100 = 30 + (-70)

150X - 100 = -40

Adding 100 to both sides:

150X = 60

Dividing both sides by 150:

X = 60/150

Simplifying the fraction:

X = 2/5