Basic Math Examples

$5 n^{2} = 4 n^{2} - 4 n$

Step 1

Since $n$ is on the right side of the equation, switch the sides so it is on the left side of the equation.

$4 n^{2} - 4 n = 5 n^{2}$

Step 2

Move all terms containing $n$ to the left side of the equation.

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Step 2.1

Subtract $5 n^{2}$ from both sides of the equation.

$4 n^{2} - 4 n - 5 n^{2} = 0$

Step 2.2

Subtract $5 n^{2}$ from $4 n^{2}$ .

$- n^{2} - 4 n = 0$

Step 3

Factor $- n$ out of $- n^{2} - 4 n$ .

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Step 3.1

Factor $- n$ out of $- n^{2}$ .

$- n \cdot n - 4 n = 0$

Step 3.2

Factor $- n$ out of $- 4 n$ .

$- n \cdot n - n \cdot 4 = 0$

Step 3.3

Factor $- n$ out of $- n (n) - n (4)$ .

$- n (n + 4) = 0$

Step 4

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

$n = 0$

$n + 4 = 0$

Step 5

Set $n$ equal to $0$ .

$n = 0$

Step 6

Set $n + 4$ equal to $0$ and solve for $n$ .

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Step 6.1

Set $n + 4$ equal to $0$ .

$n + 4 = 0$

Step 6.2

Subtract $4$ from both sides of the equation.

$n = - 4$

Step 7

The final solution is all the values that make $- n (n + 4) = 0$ true.

$n = 0, - 4$