Solve 3ax^2+6x+3=0

$$3 a x ^ { 2 } + 6 x + 3 = 0$$

Solve for a

$$a=-\frac{2x+1}{x^{2}}$$

$$x\neq 0$$

Steps for Solving Linear Equation

Subtract 6x from both sides. Anything subtracted from zero gives its negation.

$$3ax^{2}+3=-6x$$

Subtract 3 from both sides.

$$3ax^{2}=-6x-3$$

The equation is in standard form.

$$3x^{2}a=-6x-3$$

Divide both sides by 3x^{2}.

$$\frac{3x^{2}a}{3x^{2}}=\frac{-6x-3}{3x^{2}}$$

Dividing by 3x^{2} undoes the multiplication by 3x^{2}.

$$a=\frac{-6x-3}{3x^{2}}$$

Divide -6x-3 by 3x^{2}.

$$a=-\frac{2x+1}{x^{2}}$$

Solve for x (complex solution)

$$\left\{\begin{matrix}x=\frac{\sqrt{1-a}-1}{a}\text{; }x=-\frac{\sqrt{1-a}+1}{a}\text{, }&a\neq 0\\x=-\frac{1}{2}\text{, }&a=0\end{matrix}\right.$$

Solve for x

$$\left\{\begin{matrix}x=\frac{\sqrt{1-a}-1}{a}\text{; }x=-\frac{\sqrt{1-a}+1}{a}\text{, }&a\neq 0\text{ and }a\leq 1\\x=-\frac{1}{2}\text{, }&a=0\end{matrix}\right.$$