Solve by Factoring x^3+7x^2+12x=0

$x^{3} + 7 x^{2} + 12 x = 0$

Step 1

Factor $x$ out of $x^{3} + 7 x^{2} + 12 x$ .

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

$x \cdot x^{2} + 7 x^{2} + 12 x = 0$

Factor $x$ out of $7 x^{2}$ .

$x \cdot x^{2} + x (7 x) + 12 x = 0$

Factor $x$ out of $12 x$ .

$x \cdot x^{2} + x (7 x) + x \cdot 12 = 0$

Factor $x$ out of $x \cdot x^{2} + x (7 x)$ .

$x (x^{2} + 7 x) + x \cdot 12 = 0$

Factor $x$ out of $x (x^{2} + 7 x) + x \cdot 12$ .

$x (x^{2} + 7 x + 12) = 0$

Step 2

Factor.

Factor $x^{2} + 7 x + 12$ 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 $12$ and whose sum is $7$ .

$3, 4$

Write the factored form using these integers.

$x ((x + 3) (x + 4)) = 0$

Remove unnecessary parentheses.

$x (x + 3) (x + 4) = 0$

Step 3

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

$x = 0$

$x + 3 = 0$

$x + 4 = 0$

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 $x + 4$ equal to $0$ and solve for $x$ .

Set $x + 4$ equal to $0$ .

$x + 4 = 0$

Subtract $4$ from both sides of the equation.

$x = - 4$

Step 7

The final solution is all the values that make $x (x + 3) (x + 4) = 0$ true.

$x = 0, - 3, - 4$

Solve by Factoring x^3+7x^2+12x=0

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