Solve for x
x=0
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\left(x-4\right)x=\left(x+1\right)x
Variable x cannot be equal to any of the values -1,4 since division by zero is not defined. Multiply both sides of the equation by \left(x-4\right)\left(x+1\right), the least common multiple of x+1,x-4.
x^{2}-4x=\left(x+1\right)x
Use the distributive property to multiply x-4 by x.
x^{2}-4x=x^{2}+x
Use the distributive property to multiply x+1 by x.
x^{2}-4x-x^{2}=x
Subtract x^{2} from both sides.
-4x=x
Combine x^{2} and -x^{2} to get 0.
-4x-x=0
Subtract x from both sides.
-5x=0
Combine -4x and -x to get -5x.
x=0
Product of two numbers is equal to 0 if at least one of them is 0. Since -5 is not equal to 0, x must be equal to 0.
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