how do you solve 2(x-9)=3(x-6) by solving equations with variables on both sides  

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2(x-9)=3(x-6) okay, distribute 2 to x-9 on the left side and distribute 3 to x-6 on the right side. Then the equation will look like this: 2x-18=3x-18 subtract 2x to the other side: -18=x-18, then add 18 from the right side to the left, and x will equal to 0.