First we need to factor trinomial $ \color{blue}{ 2x^2+12x+10 } $ and than we use factored form to solve an equation $ \color{blue}{ 2x^2+12x+10 = 0} $.

Step 1: Simplify equation by dividing all coefficients by 2

$$ \begin{aligned} 2x^2+12x+10 &= 0 \,\,\, / \color{orangered}{ : 2 } \\[0.9 em ] x^2+6x+5 &=0 \end{aligned} $$

Step 1: Identify constants $ \color{blue}{ b }$ and $\color{red}{ c }$. ( $ \color{blue}{ b }$ is a number in front of the $ x $ term and $ \color{red}{ c } $ is a constant). In our case:

$$ \color{blue}{ b = 6 } ~ \text{ and } ~ \color{red}{ c = 5 }$$

Now we must discover two numbers that sum up to $ \color{blue}{ 6 } $ and multiply to $ \color{red}{ 5 } $.

Step 2: Find out pairs of numbers with a product of $\color{red}{ c = 5 }$.

PRODUCT = 5
1     5	-1     -5

Step 3: Find out which pair sums up to $\color{blue}{ b = 6 }$

PRODUCT = 5 and SUM = 6
1     5	-1     -5

Step 4: Put 1 and 5 into placeholders to get factored form.

$$ \begin{aligned} x^{2}+6x+5 & = (x + \color{orangered}{\square} )(x + \color{orangered}{\square}) \\ x^{2}+6x+5 & = (x + 1)(x + 5) \end{aligned} $$

Step 5: Set each factor to zero and solve equations.

$$ \begin{array}{ccc} \begin{aligned} x+1 &= 0 \\ x &= -1 \end{aligned} & ~ & \begin{aligned} x+5 &= 0 \\ x &= -5 \end{aligned} \end{array} $$

Quadratic Equation Solver