Solve by Factoring 2x^3+16x^2+30x=0

$2 x^{3} + 16 x^{2} + 30 x = 0$

Step 1

Factor $2 x$ out of $2 x^{3} + 16 x^{2} + 30 x$ .

Factor $2 x$ out of $2 x^{3}$ .

$2 x (x^{2}) + 16 x^{2} + 30 x = 0$

Factor $2 x$ out of $16 x^{2}$ .

$2 x (x^{2}) + 2 x (8 x) + 30 x = 0$

Factor $2 x$ out of $30 x$ .

$2 x (x^{2}) + 2 x (8 x) + 2 x (15) = 0$

Factor $2 x$ out of $2 x (x^{2}) + 2 x (8 x)$ .

$2 x (x^{2} + 8 x) + 2 x (15) = 0$

Factor $2 x$ out of $2 x (x^{2} + 8 x) + 2 x (15)$ .

$2 x (x^{2} + 8 x + 15) = 0$

Step 2

Factor.

Factor $x^{2} + 8 x + 15$ using the AC method.

Consider the form $x^{2} + b x + c$ . Find a pair of integers whose product is $c$ and whose sum is $b$ . In this case, whose product is $15$ and whose sum is $8$ .

$3, 5$

Write the factored form using these integers.

$2 x ((x + 3) (x + 5)) = 0$

Remove unnecessary parentheses.

$2 x (x + 3) (x + 5) = 0$

Step 3

If any individual factor on the left side of the equation is equal to $0$ , the entire expression will be equal to $0$ .

$x = 0$

$x + 3 = 0$

$x + 5 = 0$

Step 4

Set $x$ equal to $0$ .

$x = 0$

Step 5

Set $x + 3$ equal to $0$ and solve for $x$ .

Set $x + 3$ equal to $0$ .

$x + 3 = 0$

Subtract $3$ from both sides of the equation.

$x = - 3$

Step 6

Set $x + 5$ equal to $0$ and solve for $x$ .

Set $x + 5$ equal to $0$ .

$x + 5 = 0$

Subtract $5$ from both sides of the equation.

$x = - 5$

Step 7

The final solution is all the values that make $2 x (x + 3) (x + 5) = 0$ true.

$x = 0, - 3, - 5$

Solve by Factoring 2x^3+16x^2+30x=0

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