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x^{2}+x-6
Multiply and combine like terms.
a+b=1 ab=1\left(-6\right)=-6
Factor the expression by grouping. First, the expression needs to be rewritten as x^{2}+ax+bx-6. To find a and b, set up a system to be solved.
-1,6 -2,3
Since ab is negative, a and b have the opposite signs. Since a+b is positive, the positive number has greater absolute value than the negative. List all such integer pairs that give product -6.
-1+6=5 -2+3=1
Calculate the sum for each pair.
a=-2 b=3
The solution is the pair that gives sum 1.
\left(x^{2}-2x\right)+\left(3x-6\right)
Rewrite x^{2}+x-6 as \left(x^{2}-2x\right)+\left(3x-6\right).
x\left(x-2\right)+3\left(x-2\right)
Factor out x in the first and 3 in the second group.
\left(x-2\right)\left(x+3\right)
Factor out common term x-2 by using distributive property.
x^{2}+x-6
Combine -2x and 3x to get x.