Factor x^3+3x^2=24x+72

$x^{3} + 3 x^{2} = 24 x + 72$

Step 1

Move all the expressions to the left side of the equation.

Subtract $24 x$ from both sides of the equation.

$x^{3} + 3 x^{2} - 24 x = 72$

Subtract $72$ from both sides of the equation.

$x^{3} + 3 x^{2} - 24 x - 72 = 0$

Step 2

Factor the left side.

Factor out the greatest common factor from each group.

Group the first two terms and the last two terms.

$(x^{3} + 3 x^{2}) - 24 x - 72 = 0$

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

$x^{2} (x + 3) - 24 (x + 3) = 0$

Factor the polynomial by factoring out the greatest common factor, $x + 3$ .

$(x + 3) (x^{2} - 24) = 0$