To solve for x, we need to set the expression equal to zero:

5(x-36)(x+1)/(10x^2+3x-7) = 0

First, factor the denominator:
10x^2 + 3x - 7 = 10x^2 + 10x - 7x - 7
10x^2 + 10x - 7x - 7 = 10x(x + 1) - 7(x + 1)
10x(x + 1) - 7(x + 1) = (10x - 7)(x + 1)

Now substitute this back into the original equation:
5(x - 36)(x + 1) / ((10x - 7)(x + 1)) = 0

Now cancel out common factors to simplify the expression:
5(x - 36) / (10x - 7) = 0

Now set each factor equal to zero separately:
5(x - 36) = 0
x - 36 = 0
x = 36

10x - 7 = 0
10x = 7
x = 7/10

Therefore, the solutions for x are x = 36 and x = 7/10.