Solve -frac{sqrt{3}}{2}x^2+6sqrt{3}x

$$- \frac { \sqrt { 3 } } { 2 } x ^ { 2 } + 6 \sqrt { 3 } x$$

Evaluate

$$\frac{\sqrt{3}x\left(12-x\right)}{2}$$

Short Solution Steps

Express \left(-\frac{\sqrt{3}}{2}\right)x^{2} as a single fraction.

$$\frac{-\sqrt{3}x^{2}}{2}+6\sqrt{3}x$$

To add or subtract expressions, expand them to make their denominators the same. Multiply 6\sqrt{3}x times \frac{2}{2}.

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

Since \frac{-\sqrt{3}x^{2}}{2} and \frac{2\times 6\sqrt{3}x}{2} have the same denominator, add them by adding their numerators.

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

Do the multiplications in -\sqrt{3}x^{2}+2\times 6\sqrt{3}x.

$$\frac{-\sqrt{3}x^{2}+12\sqrt{3}x}{2}$$

Factor

$$\frac{\sqrt{3}x\left(12-x\right)}{2}$$

Solution Steps

Factor out \frac{1}{2}.

$$\frac{-\sqrt{3}x^{2}+12\sqrt{3}x}{2}$$

Consider -\sqrt{3}x^{2}+12\sqrt{3}x. Factor out \sqrt{3}x.

$$\sqrt{3}x\left(-x+12\right)$$

Rewrite the complete factored expression.

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