Solve for x
x=6
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\left(x-4\right)x=\left(x-2\right)\left(x-3\right)
Variable x cannot be equal to any of the values 2,4 since division by zero is not defined. Multiply both sides of the equation by \left(x-4\right)\left(x-2\right), the least common multiple of x-2,x-4.
x^{2}-4x=\left(x-2\right)\left(x-3\right)
Use the distributive property to multiply x-4 by x.
x^{2}-4x=x^{2}-5x+6
Use the distributive property to multiply x-2 by x-3 and combine like terms.
x^{2}-4x-x^{2}=-5x+6
Subtract x^{2} from both sides.
-4x=-5x+6
Combine x^{2} and -x^{2} to get 0.
-4x+5x=6
Add 5x to both sides.
x=6
Combine -4x and 5x to get x.
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