Set the quadratic expression equal to zero.

We need two numbers that multiply to 3 and add to -4. These numbers are -1 and -3.

$$(x-1)(x-3) = 0$$

$$x-1=0 \quad \text{or} \quad x-3=0$$ $$x=1 \quad \text{or} \quad x=3$$ $$\boxed{x=1 \text{ or } x=3}$$

We need two numbers that multiply to 6 and add to -7. These numbers are -1 and -6.

$$(x-1)(x-6) = 0$$

$$x-1=0 \quad \text{or} \quad x-6=0$$ $$x=1 \quad \text{or} \quad x=6$$ $$\boxed{x=1 \text{ or } x=6}$$

We need two numbers that multiply to 3 and add to 4. These numbers are 1 and 3.

$$(x+1)(x+3) = 0$$

$$x+1=0 \quad \text{or} \quad x+3=0$$ $$x=-1 \quad \text{or} \quad x=-3$$ $$\boxed{x=-1 \text{ or } x=-3}$$

This is a perfect square trinomial. We need two numbers that multiply to 4 and add to 4. These numbers are 2 and 2.

$$(x+2)(x+2) = 0$$ $$(x+2)^2 = 0$$

$$x+2=0$$ $$x=-2$$ $$\boxed{x=-2}$$

Here, $a=x$ and $b=4$.

$$(x-4)(x+4) = 0$$

$$x-4=0 \quad \text{or} \quad x+4=0$$ $$x=4 \quad \text{or} \quad x=-4$$ $$\boxed{x=4 \text{ or } x=-4}$$