To find \( x \) in each equation, let's solve them step by step.

**Equation 4:**
\[
(x - 2)^2 - [(2x+1)(x-3)] = -7
\]

Expand and simplify:
1. \( (x - 2)^2 = x^2 - 4x + 4 \)
2. \( (2x+1)(x-3) = 2x^2 - 6x + x - 3 = 2x^2 - 5x - 3 \)

Substitute into the equation:
\[
x^2 - 4x + 4 - (2x^2 - 5x - 3) = -7
\]

Simplify:
\[
x^2 - 4x + 4 - 2x^2 + 5x + 3 = -7
\]
\[
-x^2 + x + 7 = -7
\]

Rearrange:
\[
-x^2 + x + 14 = 0
\]

Multiply all terms by -1:
\[
x^2 - x - 14 = 0
\]

Solve this quadratic equation using the quadratic formula \( x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a} \) with \( a = 1, b = -1, c = -14 \).

\[
b^2 - 4ac = 1 + 56 = 57
\]

Solution:
\( x = \frac{1 \pm \sqrt{57}}{2} \).

---

**Equation 5:**
\[
(x + 1)^2 - (2x + 2)(x - 2) = 0
\]

Expand and simplify:
1. \( (x + 1)^2 = x^2 + 2x + 1 \)
2. \( (2x+2)(x-2) = 2x^2 - 4x + 2x - 4 = 2x^2 - 2x - 4 \)

Substitute into the equation:
\[
x^2 + 2x + 1 - (2x^2 - 2x - 4) = 0
\]

Simplify:
\[
x^2 + 2x + 1 - 2x^2 + 2x + 4 = 0
\]
\[
-x^2 + 4x + 5 = 0
\]

Change signs:
\[
x^2 - 4x - 5 = 0
\]

Factor:
\[
(x - 5)(x + 1) = 0
\]

Solution:
\( x = 5 \) or \( x = -1 \).

---

**Equation 6:**
\[
(2x + 3)^2 - 4(x - 1)^2 = 18
\]

Expand and simplify:
1. \( (2x + 3)^2 = 4x^2 + 12x + 9 \)
2. \( 4(x - 1)^2 = 4(x^2 - 2x + 1) = 4x^2 - 8x + 4 \)

Substitute into the equation:
\[
4x^2 + 12x + 9 - (4x^2 - 8x + 4) = 18
\]

Simplify:
\[
4x^2 + 12x + 9 - 4x^2 + 8x - 4 = 18
\]
\[
20x + 5 = 18
\]

Rearrange:
\[
20x = 13
\]

Solution:
\( x = \frac{13}{20} \).

---

**Equation 7:**
\[
27x^2(x + 1) - (3x + 1)^2 = -8
\]

Expand:
1. \( 27x^2(x + 1) = 27x^3 + 27x^2 \)
2. \( (3x + 1)^2 = 9x^2 + 6x + 1 \)

Substitute into the equation:
\[
27x^3 + 27x^2 - (9x^2 + 6x + 1) = -8
\]

Simplify:
\[
27x^3 + 27x^2 - 9x^2 - 6x - 1 = -8
\]
\[
27x^3 + 18x^2 - 6x - 1 = -8
\]

Rearrange:
\[
27x^3 + 18x^2 - 6x + 7 = 0
\]

Solution (find numerically or factor if possible).

---

**Equation 8:**
\[
(3x + 3)^2 - 4(x - 1)^2 = 0
\]

Expand:
1. \( (3x + 3)^2 = 9x^2 + 18x + 9 \)
2. \( 4(x - 1)^2 = 4(x^2 - 2x + 1) = 4x^2 - 8x + 4 \)

Substitute into the equation:
\[
9x^2 + 18x + 9 - (4x^2 - 8x + 4) = 0
\]

Simplify:
\[
9x^2 + 18x + 9 - 4x^2 + 8x - 4 = 0
\]
\[
5x^2 + 26x + 5 = 0
\]

Solve using the quadratic formula with \( a = 5, b = 26, c = 5 \).

Discriminant:
\( b^2 - 4ac = 676 - 100 = 576 \)

Solution:
\( x = \frac{-26 \pm 24}{10} \), which gives \( x_1 = -\frac{1}{5} \), and \( x_2 = -5 \).