# How do you factor and solve 3x^2+5x+2=0?

May 24, 2016

The solutions for the equation are

color(green)(x = -2/3

color(green)(x = -1

#### Explanation:

$3 {x}^{2} + 5 x + 2 = 0$

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:

${N}_{1} \cdot {N}_{2} = a \cdot c = 3 \cdot 2 = 6$

AND

${N}_{1} + {N}_{2} = b = 5$

After trying out a few numbers we get ${N}_{1} = 3$ and ${N}_{2} = 2$
$3 \cdot 2 = 6$, and $3 + 2 = 5$

Factorising the expression:

$3 {x}^{2} + \textcolor{b l u e}{5 x} + 2 = 3 {x}^{2} + \textcolor{b l u e}{3 x + 2 x} + 2$

$= 3 x \left(x + 1\right) + 2 \left(x + 1\right)$

$\left(x + 1\right)$ is a common factor to each of the terms

=color(blue)((3x + 2 ) ( x + 1 )

We now equate the factors to zero to obtain the solutions:

• 3x + 2 = 0, color(green)(x = -2/3

• x +1 = 0, color(green)(x = -1