Solve 1/2n*[-3+(-5n+2)]

$$\frac { 1 } { 2 } n \times [ - 3 + ( - 5 n + 2 ) ]$$

Evaluate

$$-\frac{n\left(5n+1\right)}{2}$$

Solution Steps

Add -3 and 2 to get -1.

$$\frac{1}{2}n\left(-1-5n\right)$$

Use the distributive property to multiply \frac{1}{2}n by -1-5n.

$$\frac{1}{2}n\left(-1\right)+\frac{1}{2}n\left(-5\right)n$$

Multiply n and n to get n^{2}.

$$\frac{1}{2}n\left(-1\right)+\frac{1}{2}n^{2}\left(-5\right)$$

Multiply \frac{1}{2} and -1 to get -\frac{1}{2}.

$$-\frac{1}{2}n+\frac{1}{2}n^{2}\left(-5\right)$$

Multiply \frac{1}{2} and -5 to get \frac{-5}{2}.

$$-\frac{1}{2}n+\frac{-5}{2}n^{2}$$

Fraction \frac{-5}{2} can be rewritten as -\frac{5}{2} by extracting the negative sign.

$$-\frac{1}{2}n-\frac{5}{2}n^{2}$$

Expand

$$\frac{-5n^{2}-n}{2}$$

Solution Steps

Add -3 and 2 to get -1.

$$\frac{1}{2}n\left(-1-5n\right)$$

Use the distributive property to multiply \frac{1}{2}n by -1-5n.

$$\frac{1}{2}n\left(-1\right)+\frac{1}{2}n\left(-5\right)n$$

Multiply n and n to get n^{2}.

$$\frac{1}{2}n\left(-1\right)+\frac{1}{2}n^{2}\left(-5\right)$$

Multiply \frac{1}{2} and -1 to get -\frac{1}{2}.

$$-\frac{1}{2}n+\frac{1}{2}n^{2}\left(-5\right)$$

Multiply \frac{1}{2} and -5 to get \frac{-5}{2}.

$$-\frac{1}{2}n+\frac{-5}{2}n^{2}$$

Fraction \frac{-5}{2} can be rewritten as -\frac{5}{2} by extracting the negative sign.

$$-\frac{1}{2}n-\frac{5}{2}n^{2}$$