Answer:
x = 3, -2
Step-by-step explanation:
To help us factor, we can split the middle term up into the sum of the terms -3x and 2x:
[tex]x^2+(-3x)+2x-6=0[/tex]
From there, we can factor out an x from the first two term and a 2 from the last two to obtain the equation
[tex]x(x-3)+2(x-3)=0[/tex]
Factoring out an (x - 3) from each term gives us the equation
[tex](x-3)(x+2)=0[/tex]
At this point, we can divide by either x - 3 or x + 2 to obtain the two equations
[tex]x-3=0[/tex] and [tex]x+2=0[/tex]
Solving both for x gives us the solutions x = 3 and x = -2. We can verify these by substituting them back into the original equation:
[tex]3^2-3-6=0\\9-3-6=0\\6-6=0\\0=0[/tex]
[tex](-2)^2-(-2)-6 = 0\\4+2-6=0\\6-6=0\\0=0[/tex]
