X(x-1)=72

To solve the equation x(x-1) = 72, we can start by expanding the left side:

x^2 - x = 72

Next, we can move all terms to one side to have a quadratic equation:

x^2 - x - 72 = 0

Now, we can try factoring the quadratic expression. We need to find two numbers that multiply to -72 and add up to -1. After some trial and error, we find that -9 and 8 fit these criteria:

(x - 9)(x + 8) = 0

Setting each factor equal to zero, we get:

x - 9 = 0 or x + 8 = 0

Solving for x in each equation gives us:

x = 9 or x = -8

So, the solutions to the equation x(x-1) = 72 are x = 9 and x = -8.