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5\left(x-2\right)-4\left(x-3\right)=5\left(x+2\right)
Multiply both sides of the equation by 20, the least common multiple of 4,5.
5x-10-4\left(x-3\right)=5\left(x+2\right)
Use the distributive property to multiply 5 by x-2.
5x-10-4x+12=5\left(x+2\right)
Use the distributive property to multiply -4 by x-3.
x-10+12=5\left(x+2\right)
Combine 5x and -4x to get x.
x+2=5\left(x+2\right)
Add -10 and 12 to get 2.
x+2=5x+10
Use the distributive property to multiply 5 by x+2.
x+2-5x=10
Subtract 5x from both sides.
-4x+2=10
Combine x and -5x to get -4x.
-4x=10-2
Subtract 2 from both sides.
-4x=8
Subtract 2 from 10 to get 8.
x=\frac{8}{-4}
Divide both sides by -4.
x=-2
Divide 8 by -4 to get -2.