# How do you factor and solve 3x^2+6x+3=0?

May 23, 2015

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

We can Split the Middle Term of this expression to factorise it.

In this technique, if we have to factorise an expression like $a {x}^{2} + b x + c$, we need to think of 2 numbers such that:

${N}_{1} \cdot {N}_{2} = a \cdot c = 3 \cdot 3 = 9$
and
${N}_{1} + {N}_{2} = b = 6$

After trying out a few numbers we get ${N}_{1} = 3$ and ${N}_{2} = 3$
$3 \cdot 3 = 9$, and $3 + 3 = 6$

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

$= 3 x \left(x + 1\right) + 3 \left(x + 1\right)$

color(green)((3x+3)(x+1) is the factorised form.

Dec 17, 2015

$x = - 1$

#### Explanation:

Factor a $3$ out.

$3 \left({x}^{2} + 2 x + 1\right) = 0$

Realize that the inner portion is a perfect binomial square, equal to ${\left(x + 1\right)}^{2}$.

$3 {\left(x + 1\right)}^{2} = 0$

Now, to solve for $0$, realize that ${\left(x + 1\right)}^{2}$ must equal to $0$ in order for the entire expression to be equal to $0$, since $3 \times 0 = 0$.

${\left(x + 1\right)}^{2} = 0$
$x + 1 = 0$
$x = - 1$

You can check this by graphing the equation. The graph should touch the $x$-axis at $x = - 1$.

graph{3x^2+6x+3 [-10.41, 12.09, -2.56, 8.7]}