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x^{2}-x-6=\left(x+3\right)\left(x-2\right)
Use the distributive property to multiply x+2 by x-3 and combine like terms.
x^{2}-x-6=x^{2}+x-6
Use the distributive property to multiply x+3 by x-2 and combine like terms.
x^{2}-x-6-x^{2}=x-6
Subtract x^{2} from both sides.
-x-6=x-6
Combine x^{2} and -x^{2} to get 0.
-x-6-x=-6
Subtract x from both sides.
-2x-6=-6
Combine -x and -x to get -2x.
-2x=-6+6
Add 6 to both sides.
-2x=0
Add -6 and 6 to get 0.
x=0
Product of two numbers is equal to 0 if at least one of them is 0. Since -2 is not equal to 0, x must be equal to 0.