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

Step 1: We can simplify equation by multiplying both sides by -1. After multiplying we have the following equation:

$$ \begin{aligned} -2x^2-10x+12 &= 0 \,\,\, / \color{orangered}{\cdot \, -1 } \\[0.9 em ] 2x^2+10x-12 &=0 \end{aligned} $$

Step 2: Simplify equation by dividing all coefficients by 2

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

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:

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

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

Step 2: Find out pairs of numbers with a product of $\color{red}{ c = -6 }$.

PRODUCT = -6
-1     6	1     -6
-2     3	2     -3

Step 3: Find out which pair sums up to $\color{blue}{ b = 5 }$

PRODUCT = -6 and SUM = 5
-1     6	1     -6
-2     3	2     -3

Step 4: Put -1 and 6 into placeholders to get factored form.

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

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

$$ \begin{array}{ccc} \begin{aligned} x-1 &= 0 \\ x &= 1 \end{aligned} & ~ & \begin{aligned} x+6 &= 0 \\ x &= -6 \end{aligned} \end{array} $$

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