Solve for x 6x=-12x^2

$6 x = - 12 x^{2}$

Step 1

Add $12 x^{2}$ to both sides of the equation.

$6 x + 12 x^{2} = 0$

Step 2

Factor the left side of the equation.

Let $u = x$ . Substitute $u$ for all occurrences of $x$ .

$6 u + 12 u^{2} = 0$

Factor $6 u$ out of $6 u + 12 u^{2}$ .

Factor $6 u$ out of $6 u$ .

$6 u (1) + 12 u^{2} = 0$

Factor $6 u$ out of $12 u^{2}$ .

$6 u (1) + 6 u (2 u) = 0$

Factor $6 u$ out of $6 u (1) + 6 u (2 u)$ .

$6 u (1 + 2 u) = 0$

Replace all occurrences of $u$ with $x$ .

$6 x (1 + 2 x) = 0$

Step 3

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

$x = 0$

$1 + 2 x = 0$

Step 4

Set $x$ equal to $0$ .

$x = 0$

Step 5

Set $1 + 2 x$ equal to $0$ and solve for $x$ .

Set $1 + 2 x$ equal to $0$ .

$1 + 2 x = 0$

Solve $1 + 2 x = 0$ for $x$ .

Subtract $1$ from both sides of the equation.

$2 x = - 1$

Divide each term in $2 x = - 1$ by $2$ and simplify.

Divide each term in $2 x = - 1$ by $2$ .

$\frac{2 x}{2} = \frac{- 1}{2}$

Simplify the left side.

Cancel the common factor of $2$ .

Cancel the common factor.

$\frac{2 x}{2} = \frac{- 1}{2}$

Divide $x$ by $1$ .

$x = \frac{- 1}{2}$

Simplify the right side.

Move the negative in front of the fraction.

$x = - \frac{1}{2}$

Step 6

The final solution is all the values that make $6 x (1 + 2 x) = 0$ true.

$x = 0, - \frac{1}{2}$

Step 7

The result can be shown in multiple forms.

Exact Form:

$x = 0, - \frac{1}{2}$

Decimal Form:

$x = 0, - 0.5$

Solve for x 6x=-12x^2

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