Final answer:
The x-intercepts of the equation (5x+3)(3x-2)=0 are x = -3/5 and x = 2/3. This is found by setting each factor equal to zero and solving for x.
Step-by-step explanation:
To find the x-intercepts of the equation (5x+3)(3x-2)=0, we need to set each factor equal to zero and solve for x. This is because if a product equals zero, at least one of the factors must be zero. There are two factors in this equation, and setting each one to zero gives us two separate equations to solve: 5x + 3 = 0 and 3x - 2 = 0.
For the first equation, 5x + 3 = 0, we subtract 3 from both sides to get 5x = -3 and then divide both sides by 5 to find x = -3/5.
For the second equation, 3x - 2 = 0, we add 2 to both sides to get 3x = 2 and then divide both sides by 3 to find x = 2/3.
Therefore, the x-intercepts are x = -3/5 and x = 2/3.