((x-5)(x+5)-(x-2)^3-7x^2+(x+1)(x^2-x+1)=(x+3)^3-(x^3+9x^2)\), \((x-4)^3-(x-5)(x^2+5x+25)=(x-2)(x^2-2x+4)-(x+4)^3-(x-7)\), \((x+1)^3-(x+3)(x^2-3x+9)=(x-3)^3+3(2x+1)^2-(x^3-5x+1)\)

To solve the equations in the image, you will need to simplify each expression on the left-hand side and right-hand side, equate them, and find any potential values for \(x\) if required. I can guide you through the process for a specific equation, or help simplify if you'd like!

For example, let's take the first expression:

\[
(x-5)(x+5)-(x-2)^3-7x^2+(x+1)(x^2-x+1)=(x+3)^3-(x^3+9x^2)
\]

### Step 1: Simplify the Left-Hand Side (LHS)

1. **Expand each term**:
- \((x-5)(x+5) = x^2 - 25\)
- \(-(x-2)^3 = -[(x^3 - 6x^2 + 12x - 8)] = -x^3 + 6x^2 - 12x + 8\)
- \(-7x^2\) remains as is.
- \((x+1)(x^2-x+1) = x^3 - x^2 + x + x^2 - x + 1 = x^3 + 1\)

2. **Combine into LHS**:
\[
(x^2 - 25) + (-x^3 + 6x^2 - 12x + 8) - 7x^2 + (x^3 + 1)
\]
Combine like terms:
- \(x^3\) cancels out,
- \(6x^2 - 7x^2 + x^2= 0\),
- \(-12x\),
- \(-25 + 8 + 1 = -16\).

So, LHS simplifies to:
\[
-12x - 16
\]

### Step 2: Simplify the Right-Hand Side (RHS)

1. **Expand**:
- \((x+3)^3 = x^3 + 9x^2 + 27\)
- \(-(x^3 + 9x^2) = -x^3 - 9x^2\)

2. **Combine into RHS**:
\[
(x^3 + 9x^2 + 27) - (x^3 + 9x^2) = 27
\]

### Step 3: Set LHS equal to RHS

Now you have:
\[
-12x - 16 = 27
\]

### Step 4: Solve for \(x\)

1. Add 16 to both sides:
\[
-12x = 27 + 16
\]
\[
-12x = 43
\]

2. Divide by -12:
\[
x = -\frac{43}{12}
\]

Let me know if you want to go through another equation or need further assistance!