Solve the following quadratic equations: a) (x−4)(x+7)=0, b) (2x)(x+8)=0, d) x2=37, e) 9x2=25, f) 4x2=4, h) x2=32, i) 20=x2+4

$$x = 4 \quad \text{or} \quad x = -7$$

The solutions are $\boxed{x = 4, -7}$.

$$x = 0 \quad \text{or} \quad x = -8$$

The solutions are $\boxed{x = 0, -8}$.

$$x^2 - 12 + 12 = 37 + 12$$ $$x^2 = 49$$

$$x = \pm\sqrt{49}$$ $$x = \pm 7$$

The solutions are $\boxed{x = 7, -7}$.

$$\frac{9x^2}{9} = \frac{25}{9}$$ $$x^2 = \frac{25}{9}$$

$$x = \pm\sqrt{\frac{25}{9}}$$ $$x = \pm\frac{5}{3}$$

The solutions are $\boxed{x = \frac{5}{3}, -\frac{5}{3}}$.

$$\frac{4x^2}{4} = \frac{4}{4}$$ $$x^2 = 1$$

$$x = \pm\sqrt{1}$$ $$x = \pm 1$$

The solutions are $\boxed{x = 1, -1}$.

$$x^2 - 4 + 4 = 32 + 4$$ $$x^2 = 36$$

$$x = \pm\sqrt{36}$$ $$x = \pm 6$$

The solutions are $\boxed{x = 6, -6}$.

$$20 - 4 = x^2 + 4 - 4$$ $$16 = x^2$$

$$x = \pm\sqrt{16}$$ $$x = \pm 4$$

The solutions are $\boxed{x = 4, -4}$.

j)

$$5x^2 + 2 - 2 = 7 - 2$$ $$5x^2 = 5$$

$$\frac{5x^2}{5} = \frac{5}{5}$$ $$x^2 = 1$$

$$x = \pm\sqrt{1}$$ $$x = \pm 1$$

The solutions are $\boxed{x = 1, -1}$.