Solve by Factoring 2x^3+10x^2+12x=0

$2 x^{3} + 10 x^{2} + 12 x = 0$

Step 1

Factor $2 x$ out of $2 x^{3} + 10 x^{2} + 12 x$ .

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

$2 x (x^{2}) + 10 x^{2} + 12 x = 0$

Factor $2 x$ out of $10 x^{2}$ .

$2 x (x^{2}) + 2 x (5 x) + 12 x = 0$

Factor $2 x$ out of $12 x$ .

$2 x (x^{2}) + 2 x (5 x) + 2 x (6) = 0$

Factor $2 x$ out of $2 x (x^{2}) + 2 x (5 x)$ .

$2 x (x^{2} + 5 x) + 2 x (6) = 0$

Factor $2 x$ out of $2 x (x^{2} + 5 x) + 2 x (6)$ .

$2 x (x^{2} + 5 x + 6) = 0$

Step 2

Factor.

Factor $x^{2} + 5 x + 6$ 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 $6$ and whose sum is $5$ .

$2, 3$

Write the factored form using these integers.

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

Remove unnecessary parentheses.

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

Step 3

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

$x = 0$

$x + 2 = 0$

$x + 3 = 0$

Step 4

Set $x$ equal to $0$ .

$x = 0$

Step 5

Set $x + 2$ equal to $0$ and solve for $x$ .

Set $x + 2$ equal to $0$ .

$x + 2 = 0$

Subtract $2$ from both sides of the equation.

$x = - 2$

Step 6

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 7

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

$x = 0, - 2, - 3$

Solve by Factoring 2x^3+10x^2+12x=0

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