(x-2)(x-3)=6

To solve the given quadratic equation \((x-2)(x-3)=6\), we can first expand the left side of the equation using the distributive property: \((x-2)(x-3)=x^2 - 3x - 2x + 6 = x^2 - 5x + 6\) Now, we have the equation \(x^2 - 5x + 6 = 6\). Next, we can simplify this equation by subtracting 6 from both sides: \(x^2 - 5x = 0\) Factor out an \(x\) from the left side of the equation: \(x(x - 5) = 0\) This equation can be satisfied when either \(x = 0\) or \(x - 5 = 0\). So, the solutions for the equation \((x-2)(x-3)=6\) are \(x = 0\) or \(x = 5\).