x(x-1)=72

To solve the equation x(x-1) = 72, we need to expand the equation and then set it equal to zero.

First, distribute the x to both terms within the parentheses:

x^2 - x = 72

Next, move the constant term to the left side of the equation by subtracting 72 from both sides:

x^2 - x - 72 = 0

Now we have a quadratic equation in standard form. To solve this type of equation, we can either factor it, complete the square, or use the quadratic formula.

Let's try factoring:

The factors of -72 that add up to -1 are 9 and -8, so we can rewrite the equation as:

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

Setting each factor equal to zero, we have two possible solutions:

x + 9 = 0 or x - 8 = 0

Solving each equation separately:

x + 9 = 0 => x = -9

x - 8 = 0 => x = 8

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