Solve for n (5n-7)(n-7)=0

$(5 n - 7) (n - 7) = 0$

Step 1

If any individual factor on the left side of the equation is equal to $0$ , the entire expression will be equal to $0$ .

$5 n - 7 = 0$

$n - 7 = 0$

Step 2

Set $5 n - 7$ equal to $0$ and solve for $n$ .

Set $5 n - 7$ equal to $0$ .

$5 n - 7 = 0$

Solve $5 n - 7 = 0$ for $n$ .

Add $7$ to both sides of the equation.

$5 n = 7$

Divide each term in $5 n = 7$ by $5$ and simplify.

Divide each term in $5 n = 7$ by $5$ .

$\frac{5 n}{5} = \frac{7}{5}$

Simplify the left side.

Cancel the common factor of $5$ .

Cancel the common factor.

$\frac{5 n}{5} = \frac{7}{5}$

Divide $n$ by $1$ .

$n = \frac{7}{5}$

Step 3

Set $n - 7$ equal to $0$ and solve for $n$ .

Set $n - 7$ equal to $0$ .

$n - 7 = 0$

Add $7$ to both sides of the equation.

$n = 7$

Step 4

The final solution is all the values that make $(5 n - 7) (n - 7) = 0$ true.

$n = \frac{7}{5}, 7$

Step 5

The result can be shown in multiple forms.

Exact Form:

$n = \frac{7}{5}, 7$

Decimal Form:

$n = 1.4, 7$

Mixed Number Form:

$n = 1 \frac{2}{5}, 7$