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