The problem is to solve the quadratic equation $7x^2 + 42x - 49 = 0$ by factoring.

1. Problem Description

The problem is to solve the quadratic equation $7x^2 + 42x - 49 = 0$ by factoring.

2. Solution Steps

First, we can divide the entire equation by 7 to simplify it:

$x^2 + 6x - 7 = 0$

Now, we need to factor the quadratic expression $x^2 + 6x - 7$. We are looking for two numbers that multiply to -7 and add up to

6. These numbers are 7 and -

1. So, we can factor the quadratic expression as $(x + 7)(x - 1)$.

Thus, the equation becomes $(x + 7)(x - 1) = 0$.

Now, we set each factor equal to zero and solve for $x$:

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

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

3. Final Answer

The solutions are $x = -7$ and $x = 1$.