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3x-3=-\left(x+3\right)
Multiply both sides of the equation by 4, the least common multiple of 4,-4.
3x-3=-x-3
To find the opposite of x+3, find the opposite of each term.
3x-3+x=-3
Add x to both sides.
4x-3=-3
Combine 3x and x to get 4x.
4x=-3+3
Add 3 to both sides.
4x=0
Add -3 and 3 to get 0.
x=0
Product of two numbers is equal to 0 if at least one of them is 0. Since 4 is not equal to 0, x must be equal to 0.