Explain in english

Let $M_E$ be the mass of the Earth and $M_M$ be the mass of the Moon.
We are given $M_E = 80 M_M$.
Let $D$ be the distance between the centers of the Earth and the Moon, $D = 4.0 \times 10^5 \text{ km}$.
Let $x$ be the distance from the center of the Earth to the point where the resultant gravitational field is zero.
The distance from the center of the Moon to this point will then be $D - x$.
The gravitational field $g$ due to a mass $M$ at a distance $r$ is given by the formula $g = \frac{GM}{r^2}$, where $G$ is the gravitational constant.
For the resultant field to be zero, the magnitudes of the gravitational fields from the Earth ($g_E$) and the Moon ($g_M$) must be equal: $g_E = g_M$.

We can cancel the gravitational constant $G$ from both sides.

Using the relationship $M_E = 80 M_M$:

We can cancel $M_M$ from both sides:

Take the square root of both sides (we consider the positive root since $x$ is a distance):

We know that $\sqrt{80} = \sqrt{16 \times 5} = 4\sqrt{5}$.

Cross-multiply to isolate $x$:

Group the terms with $x$:

Substitute the value of $D = 4.0 \times 10^5 \text{ km}$:

Calculate the numerical value of $\frac{4\sqrt{5}}{1 + 4\sqrt{5}}$:

Now, multiply by $D$:

Rounding to two significant figures, as per the given $D = 4.0 \times 10^5 \text{ km}$:

The distance from the center of the Earth where the resultant gravitational field is zero is: