Factor 4x^(3/2)(x^3+x^2)-6x^(5/2)-6x^(3/2)

$4 x^{\frac{3}{2}} (x^{3} + x^{2}) - 6 x^{\frac{5}{2}} - 6 x^{\frac{3}{2}}$

Factor $2 x^{\frac{3}{2}}$ out of $4 x^{\frac{3}{2}} (x^{3} + x^{2}) - 6 x^{\frac{5}{2}} - 6 x^{\frac{3}{2}}$ .

Factor $2 x^{\frac{3}{2}}$ out of $4 x^{\frac{3}{2}} (x^{3} + x^{2})$ .

$2 x^{\frac{3}{2}} (2 (x^{3} + x^{2})) - 6 x^{\frac{5}{2}} - 6 x^{\frac{3}{2}}$

Factor $2 x^{\frac{3}{2}}$ out of $- 6 x^{\frac{5}{2}}$ .

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

Factor $2 x^{\frac{3}{2}}$ out of $- 6 x^{\frac{3}{2}}$ .

$2 x^{\frac{3}{2}} (2 (x^{3} + x^{2})) + 2 x^{\frac{3}{2}} (- 3 x^{\frac{2}{2}}) + 2 x^{\frac{3}{2}} (- 3)$

Factor $2 x^{\frac{3}{2}}$ out of $2 x^{\frac{3}{2}} (2 (x^{3} + x^{2})) + 2 x^{\frac{3}{2}} (- 3 x^{\frac{2}{2}})$ .

$2 x^{\frac{3}{2}} (2 (x^{3} + x^{2}) - 3 x^{\frac{2}{2}}) + 2 x^{\frac{3}{2}} (- 3)$

Factor $2 x^{\frac{3}{2}}$ out of $2 x^{\frac{3}{2}} (2 (x^{3} + x^{2}) - 3 x^{\frac{2}{2}}) + 2 x^{\frac{3}{2}} (- 3)$ .

$2 x^{\frac{3}{2}} (2 (x^{3} + x^{2}) - 3 x^{\frac{2}{2}} - 3)$

Apply the distributive property.

$2 x^{\frac{3}{2}} (2 x^{3} + 2 x^{2} - 3 x^{\frac{2}{2}} - 3)$

Divide $2$ by $2$ .

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

Simplify.

$2 x^{\frac{3}{2}} (2 x^{3} + 2 x^{2} - 3 x - 3)$

Factor.

Rewrite $2 x^{3} + 2 x^{2} - 3 x - 3$ in a factored form.

Factor out the greatest common factor from each group.

Group the first two terms and the last two terms.

$2 x^{\frac{3}{2}} ((2 x^{3} + 2 x^{2}) - 3 x - 3)$

Factor out the greatest common factor (GCF) from each group.

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

Factor the polynomial by factoring out the greatest common factor, $x + 1$ .

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

Remove unnecessary parentheses.

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