Solve 3*1/6((3*2+x)2+(2x+3)*(9-x))

$$3 \times \frac{ 1 }{ 6 } ((3 \times 2+x)2+(2x+3) \times (9-x))$$

Evaluate

$$-x^{2}+\frac{17x}{2}+\frac{39}{2}$$

Solution Steps

Multiply 3 and \frac{1}{6} to get \frac{3}{6}.

$$\frac{3}{6}\left(\left(3\times 2+x\right)\times 2+\left(2x+3\right)\left(9-x\right)\right)$$

Reduce the fraction \frac{3}{6} to lowest terms by extracting and canceling out 3.

$$\frac{1}{2}\left(\left(3\times 2+x\right)\times 2+\left(2x+3\right)\left(9-x\right)\right)$$

Multiply 3 and 2 to get 6.

$$\frac{1}{2}\left(\left(6+x\right)\times 2+\left(2x+3\right)\left(9-x\right)\right)$$

Use the distributive property to multiply 6+x by 2.

$$\frac{1}{2}\left(12+2x+\left(2x+3\right)\left(9-x\right)\right)$$

Apply the distributive property by multiplying each term of 2x+3 by each term of 9-x.

$$\frac{1}{2}\left(12+2x+18x-2x^{2}+27-3x\right)$$

Combine 18x and -3x to get 15x.

$$\frac{1}{2}\left(12+2x+15x-2x^{2}+27\right)$$

Combine 2x and 15x to get 17x.

$$\frac{1}{2}\left(12+17x-2x^{2}+27\right)$$

Add 12 and 27 to get 39.

$$\frac{1}{2}\left(39+17x-2x^{2}\right)$$

Use the distributive property to multiply \frac{1}{2} by 39+17x-2x^{2}.

$$\frac{1}{2}\times 39+\frac{1}{2}\times 17x+\frac{1}{2}\left(-2\right)x^{2}$$

Multiply \frac{1}{2} and 39 to get \frac{39}{2}.

$$\frac{39}{2}+\frac{1}{2}\times 17x+\frac{1}{2}\left(-2\right)x^{2}$$

Multiply \frac{1}{2} and 17 to get \frac{17}{2}.

$$\frac{39}{2}+\frac{17}{2}x+\frac{1}{2}\left(-2\right)x^{2}$$

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

$$\frac{39}{2}+\frac{17}{2}x+\frac{-2}{2}x^{2}$$

Divide -2 by 2 to get -1.

$$\frac{39}{2}+\frac{17}{2}x-x^{2}$$

Expand

$$-x^{2}+\frac{17x}{2}+\frac{39}{2}$$

Solution Steps

Multiply 3 and \frac{1}{6} to get \frac{3}{6}.

$$\frac{3}{6}\left(\left(3\times 2+x\right)\times 2+\left(2x+3\right)\left(9-x\right)\right)$$

Reduce the fraction \frac{3}{6} to lowest terms by extracting and canceling out 3.

$$\frac{1}{2}\left(\left(3\times 2+x\right)\times 2+\left(2x+3\right)\left(9-x\right)\right)$$

Multiply 3 and 2 to get 6.

$$\frac{1}{2}\left(\left(6+x\right)\times 2+\left(2x+3\right)\left(9-x\right)\right)$$

Use the distributive property to multiply 6+x by 2.

$$\frac{1}{2}\left(12+2x+\left(2x+3\right)\left(9-x\right)\right)$$

Apply the distributive property by multiplying each term of 2x+3 by each term of 9-x.

$$\frac{1}{2}\left(12+2x+18x-2x^{2}+27-3x\right)$$

Combine 18x and -3x to get 15x.

$$\frac{1}{2}\left(12+2x+15x-2x^{2}+27\right)$$

Combine 2x and 15x to get 17x.

$$\frac{1}{2}\left(12+17x-2x^{2}+27\right)$$

Add 12 and 27 to get 39.

$$\frac{1}{2}\left(39+17x-2x^{2}\right)$$

Use the distributive property to multiply \frac{1}{2} by 39+17x-2x^{2}.

$$\frac{1}{2}\times 39+\frac{1}{2}\times 17x+\frac{1}{2}\left(-2\right)x^{2}$$

Multiply \frac{1}{2} and 39 to get \frac{39}{2}.

$$\frac{39}{2}+\frac{1}{2}\times 17x+\frac{1}{2}\left(-2\right)x^{2}$$

Multiply \frac{1}{2} and 17 to get \frac{17}{2}.

$$\frac{39}{2}+\frac{17}{2}x+\frac{1}{2}\left(-2\right)x^{2}$$

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

$$\frac{39}{2}+\frac{17}{2}x+\frac{-2}{2}x^{2}$$

Divide -2 by 2 to get -1.

$$\frac{39}{2}+\frac{17}{2}x-x^{2}$$