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2\left(2x-3\right)=-x-3-3
Multiply both sides of the equation by 8, the least common multiple of 4,8.
4x-6=-x-3-3
Use the distributive property to multiply 2 by 2x-3.
4x-6=-x-6
Subtract 3 from -3 to get -6.
4x-6+x=-6
Add x to both sides.
5x-6=-6
Combine 4x and x to get 5x.
5x=-6+6
Add 6 to both sides.
5x=0
Add -6 and 6 to get 0.
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.