Solve [x^3/3-7x^2/2+6x)

$$[ \frac { x ^ { 3 } } { 3 } - \frac { 7 x ^ { 2 } } { 2 } + 6 x )$$

Evaluate

$$\frac{x^{3}}{3}-\frac{7x^{2}}{2}+6x$$

Short Solution Steps

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of 3 and 2 is 6. Multiply \frac{x^{3}}{3} times \frac{2}{2}. Multiply \frac{7x^{2}}{2} times \frac{3}{3}.

$$\frac{2x^{3}}{6}-\frac{3\times 7x^{2}}{6}+6x$$

Since \frac{2x^{3}}{6} and \frac{3\times 7x^{2}}{6} have the same denominator, subtract them by subtracting their numerators.

$$\frac{2x^{3}-3\times 7x^{2}}{6}+6x$$

Do the multiplications in 2x^{3}-3\times 7x^{2}.

$$\frac{2x^{3}-21x^{2}}{6}+6x$$

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

$$\frac{2x^{3}-21x^{2}}{6}+\frac{6\times 6x}{6}$$

Since \frac{2x^{3}-21x^{2}}{6} and \frac{6\times 6x}{6} have the same denominator, add them by adding their numerators.

$$\frac{2x^{3}-21x^{2}+6\times 6x}{6}$$

Do the multiplications in 2x^{3}-21x^{2}+6\times 6x.

$$\frac{2x^{3}-21x^{2}+36x}{6}$$

Factor

$$\frac{x\left(x-\frac{21-3\sqrt{17}}{4}\right)\left(x-\frac{3\sqrt{17}+21}{4}\right)}{3}$$