Final answer:
The equation (x-5)(2x-1)(2x+3) is solved by finding the values of x where any of the factors is zero, which gives the solutions x=5, x=0.5, and x=-1.5.
Step-by-step explanation:
The equation to solve is (x-5)(2x-1)(2x+3). To solve this equation, we need to find the values of x for which the equation equals zero. The equation is a product of three factors, and a product equals zero if and only if at least one of the factors is zero. Therefore, we can set each factor equal to zero and solve for x.
First factor: x-5 = 0 leads to x = 5.
Second factor: 2x-1 = 0 leads to x = 1/2 or x = 0.5.
Third factor: 2x+3 = 0 leads to x = -3/2 or x = -1.5.
Thus, the solutions to the equation are x=5, x=0.5, and x=-1.5.