y=4(4x3-3x2-1) Y=2x3+1 x2

It looks like you are working with two equations. Let’s analyze them:

1. Equation 1: \( y = 4(4x^3 - 3x^2 - 1) \)
2. Equation 2: \( y = 2x^3 + 1 \)

It seems you might want to find the points of intersection between these two equations or analyze them in some way.

To find the points of intersection, we can set the two equations equal to each other:

\[ 4(4x^3 - 3x^2 - 1) = 2x^3 + 1 \]

Next, simplify and rearrange this equation:

1. Expand the left-hand side: \[ 16x^3 - 12x^2 - 4 = 2x^3 + 1 \]

2. Move everything to one side of the equation: \[ 16x^3 - 12x^2 - 4 - 2x^3 - 1 = 0 \]

3. Combine like terms: \[ (16x^3 - 2x^3) - 12x^2 + (-4 - 1) = 0 \] \[ 14x^3 - 12x^2 - 5 = 0 \]

Now you can solve the polynomial \( 14x^3 - 12x^2 - 5 = 0 \). This may require numerical methods or graphing techniques if it doesn't factor easily.

If you need further steps or have a specific question (like finding roots or analyzing the functions), please let me know!