Solve -3/2x(-1/2+x/6-4)

$$- \frac { 3 } { 2 } x ( - \frac { 1 } { 2 } + \frac { x } { 6 } - 4 )$$

Evaluate

$$-\frac{x\left(x-27\right)}{4}$$

Short Solution Steps

Convert 4 to fraction \frac{8}{2}.

$$-\frac{3}{2}x\left(-\frac{1}{2}+\frac{x}{6}-\frac{8}{2}\right)$$

Since -\frac{1}{2} and \frac{8}{2} have the same denominator, subtract them by subtracting their numerators.

$$-\frac{3}{2}x\left(\frac{-1-8}{2}+\frac{x}{6}\right)$$

Subtract 8 from -1 to get -9.

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

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of 2 and 6 is 6. Multiply -\frac{9}{2} times \frac{3}{3}.

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

Since -\frac{9\times 3}{6} and \frac{x}{6} have the same denominator, add them by adding their numerators.

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

Do the multiplications in -9\times 3+x.

$$-\frac{3}{2}x\times \frac{-27+x}{6}$$

Multiply -\frac{3}{2} times \frac{-27+x}{6} by multiplying numerator times numerator and denominator times denominator.

$$\frac{-3\left(-27+x\right)}{2\times 6}x$$

Cancel out 3 in both numerator and denominator.

$$\frac{-\left(x-27\right)}{2\times 2}x$$

Multiply 2 and 2 to get 4.

$$\frac{-\left(x-27\right)}{4}x$$

Express \frac{-\left(x-27\right)}{4}x as a single fraction.

$$\frac{-\left(x-27\right)x}{4}$$

Use the distributive property to multiply -1 by x-27.

$$\frac{\left(-x+27\right)x}{4}$$

Use the distributive property to multiply -x+27 by x.

$$\frac{-x^{2}+27x}{4}$$

Expand

$$\frac{27x-x^{2}}{4}$$

Short Solution Steps

Convert 4 to fraction \frac{8}{2}.

$$-\frac{3}{2}x\left(-\frac{1}{2}+\frac{x}{6}-\frac{8}{2}\right)$$

Since -\frac{1}{2} and \frac{8}{2} have the same denominator, subtract them by subtracting their numerators.

$$-\frac{3}{2}x\left(\frac{-1-8}{2}+\frac{x}{6}\right)$$

Subtract 8 from -1 to get -9.

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

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of 2 and 6 is 6. Multiply -\frac{9}{2} times \frac{3}{3}.

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

Since -\frac{9\times 3}{6} and \frac{x}{6} have the same denominator, add them by adding their numerators.

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

Do the multiplications in -9\times 3+x.

$$-\frac{3}{2}x\times \frac{-27+x}{6}$$

Multiply -\frac{3}{2} times \frac{-27+x}{6} by multiplying numerator times numerator and denominator times denominator.

$$\frac{-3\left(-27+x\right)}{2\times 6}x$$

Cancel out 3 in both numerator and denominator.

$$\frac{-\left(x-27\right)}{2\times 2}x$$

Multiply 2 and 2 to get 4.

$$\frac{-\left(x-27\right)}{4}x$$

Express \frac{-\left(x-27\right)}{4}x as a single fraction.

$$\frac{-\left(x-27\right)x}{4}$$

Use the distributive property to multiply -1 by x-27.

$$\frac{\left(-x+27\right)x}{4}$$

Use the distributive property to multiply -x+27 by x.

$$\frac{-x^{2}+27x}{4}$$