Algebra Examples

$g (n) = n^{2} + 4 n$

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.

$n^{2} + 4 n = g n$

Step 2

Subtract $g n$ from both sides of the equation.

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

Step 3

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

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Step 3.1

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

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

Step 3.2

Factor $n$ out of $4 n$ .

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

Step 3.3

Factor $n$ out of $- g n$ .

$n \cdot n + n \cdot 4 + n (- g) = 0$

Step 3.4

Factor $n$ out of $n \cdot n + n \cdot 4$ .

$n (n + 4) + n (- g) = 0$

Step 3.5

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

$n (n + 4 - g) = 0$

Step 4

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

$n = 0$

$n + 4 - g = 0$

Step 5

Set $n$ equal to $0$ .

$n = 0$

Step 6

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

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Step 6.1

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

$n + 4 - g = 0$

Step 6.2

Move all terms not containing $n$ to the right side of the equation.

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Step 6.2.1

Subtract $4$ from both sides of the equation.

$n - g = - 4$

Step 6.2.2

Add $g$ to both sides of the equation.

$n = - 4 + g$

Step 7

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

$n = 0$

$n = - 4 + g$