Find the Roots (Zeros) 3x^2+36=-24x

$3 x^{2} + 36 = - 24 x$

Add $24 x$ to both sides of the equation.

$3 x^{2} + 36 + 24 x = 0$

Factor the left side of the equation.

Factor $3$ out of $3 x^{2} + 36 + 24 x$ .

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

$3 (x^{2}) + 36 + 24 x = 0$

Factor $3$ out of $36$ .

$3 x^{2} + 3 \cdot 12 + 24 x = 0$

Factor $3$ out of $24 x$ .

$3 x^{2} + 3 \cdot 12 + 3 (8 x) = 0$

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

$3 (x^{2} + 12) + 3 (8 x) = 0$

Factor $3$ out of $3 (x^{2} + 12) + 3 (8 x)$ .

$3 (x^{2} + 12 + 8 x) = 0$

Factor.

Factor $x^{2} + 12 + 8 x$ 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 $8$ .

$2, 6$

Write the factored form using these integers.

$3 ((x + 2) (x + 6)) = 0$

Remove unnecessary parentheses.

$3 (x + 2) (x + 6) = 0$

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

$x + 2 = 0$

$x + 6 = 0$

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.

$x = - 2$

Set $x + 6$ equal to $0$ and solve for $x$ .

Set $x + 6$ equal to $0$ .

$x + 6 = 0$

Subtract $6$ from both sides of the equation.

$x = - 6$

The final solution is all the values that make $3 (x + 2) (x + 6) = 0$ true.

$x = - 2, - 6$

Find the Roots (Zeros) 3x^2+36=-24x

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