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x\left(-9\right)=\left(x+1\right)\left(-6\right)
Variable x cannot be equal to any of the values -1,0 since division by zero is not defined. Multiply both sides of the equation by x\left(x+1\right), the least common multiple of x+1,x.
x\left(-9\right)=-6x-6
Use the distributive property to multiply x+1 by -6.
x\left(-9\right)+6x=-6
Add 6x to both sides.
-3x=-6
Combine x\left(-9\right) and 6x to get -3x.
x=\frac{-6}{-3}
Divide both sides by -3.
x=2
Divide -6 by -3 to get 2.