Determine Intersection Points: Solve y = (x+3)(4x-4) with X-axis

To find the points of intersection of the function $y = (x+3)(4x-4)$ with the x-axis, we set $y = 0$ and solve for $x$.

First, we set each factor of the expression to zero:

• For the first factor, $x+3 = 0$:
• Solve for $x$:
• $x + 3 = 0$
• $x = -3$
• For the second factor, $4x-4 = 0$:
• Solve for $x$:
• $4x - 4 = 0$
• $4x = 4$
• $x = 1$

The points of intersection are where these $x$ values occur with $y = 0$. Thus, the points are $(-3, 0)$ and $(1, 0)$.

Therefore, the solution to the problem is $(-3,0),(1,0)$.