Solve for n 10n^2+40n=0

$10 n^{2} + 40 n = 0$

Factor $10 n$ out of $10 n^{2} + 40 n$ .

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Factor $10 n$ out of $10 n^{2}$ .

$10 n (n) + 40 n = 0$

Factor $10 n$ out of $40 n$ .

$10 n (n) + 10 n (4) = 0$

Factor $10 n$ out of $10 n (n) + 10 n (4)$ .

$10 n (n + 4) = 0$

Divide each term by $10$ and simplify.

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Divide each term in $10 n (n + 4) = 0$ by $10$ .

$\frac{10 n (n + 4)}{10} = \frac{0}{10}$

Simplify $\frac{10 n (n + 4)}{10}$ .

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Cancel the common factor of $10$ .

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Cancel the common factor.

$\frac{10 n (n + 4)}{10} = \frac{0}{10}$

Divide $n (n + 4)$ by $1$ .

$n (n + 4) = \frac{0}{10}$

Apply the distributive property.

$n \cdot n + n \cdot 4 = \frac{0}{10}$

Simplify the expression.

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Multiply $n$ by $n$ .

$n^{2} + n \cdot 4 = \frac{0}{10}$

Move $4$ to the left of $n$ .

$n^{2} + 4 n = \frac{0}{10}$

Divide $0$ by $10$ .

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

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

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

$n \cdot n + 4 n = 0$

Factor $n$ out of $4 n$ .

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

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

$n (n + 4) = 0$

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

$n = 0$

$n + 4 = 0$

Set the first factor equal to $0$ .

$n = 0$

Set the next factor equal to $0$ and solve.

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Set the next factor equal to $0$ .

$n + 4 = 0$

Subtract $4$ from both sides of the equation.

$n = - 4$

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

$n = 0, - 4$

Solve for n 10n^2+40n=0

Solving MATH problems