The problem is to solve four equations: 1) $(6x+7)(x+1)=0$ 2) $7(n-4)(n-2)=0$ 3) $x^2+x-56=0$ 4) $x^2+5x-24=0$

1. Problem Description

The problem is to solve four equations:

1) $(6x+7)(x+1)=0$

2) $7(n-4)(n-2)=0$

3) $x^2+x-56=0$

4) $x^2+5x-24=0$

2. Solution Steps

1) $(6x+7)(x+1)=0$

This equation is already factored. We set each factor to zero:

$6x+7=0$ or $x+1=0$

$6x = -7$ or $x = -1$

$x = -\frac{7}{6}$ or $x = -1$

2) $7(n-4)(n-2)=0$

We set each factor to zero:

$7=0$ (This is not possible)

$n-4=0$ or $n-2=0$

$n=4$ or $n=2$

3) $x^2+x-56=0$

We need to factor the quadratic. We are looking for two numbers that multiply to -56 and add to

1. The numbers are 8 and -

7. $(x+8)(x-7)=0$

We set each factor to zero:

$x+8=0$ or $x-7=0$

$x=-8$ or $x=7$

4) $x^2+5x-24=0$

We need to factor the quadratic. We are looking for two numbers that multiply to -24 and add to

5. The numbers are 8 and -

3. $(x+8)(x-3)=0$

We set each factor to zero:

$x+8=0$ or $x-3=0$

$x=-8$ or $x=3$

3. Final Answer

1) $x=-\frac{7}{6}, -1$

2) $n=4, 2$

3) $x=-8, 7$

4) $x=-8, 3$