To solve the equation (6x-18) (3x+2) = 0, we can use the zero product property, which states that if the product of two numbers is zero, then at least one of the numbers must be zero. In this case, the left-hand side of the equation is the product of two numbers, (6x-18) and (3x+2), which is equal to zero. Therefore, by the zero product property, at least one of these numbers must be zero.
To find the values of x that make (6x-18) or (3x+2) equal to zero, we can set each of these expressions equal to zero and solve for x. Setting (6x-18) equal to zero, we get 6x-18 = 0, which can be rewritten as 6x = 18. Dividing both sides of the equation by 6, we get x = 3.
Similarly, setting (3x+2) equal to zero, we get 3x+2 = 0, which can be rewritten as 3x = -2. Dividing both sides of the equation by 3, we get x = -2/3.
Therefore, the values of x that make (6x-18) or (3x+2) equal to zero are x = 3 and x = -2/3. These are the solutions to the equation (6x-18) (3x+2) = 0.
Overall, the equation (6x-18) (3x+2) = 0 has two solutions: x = 3 and x = -2/3.