check math

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Here are my answers. Can you check if I got the right answers? Thank you!

(x+3)(x-3)>0 answer: x<-3 or x>3
x^2-2x-15</=0 answer: -3</=x</=5
12x^2=3x answer: x=1/4
sin2x=sinx, 0</=x</=2pi answer: x=pi
lx-3l<7 answer: (-oo,oo)
(x+1)^2(x-2)+(x+1)(x-2)^2=0
answer: x=-1,2,1/2
27^(2x)=9^(x-3)answer: x=-3/2
logx+log(x-3)=1 answer: x=-2, 5

(x+3)(x-3)>0 answer: x<-3 or x>3 ok
x^2-2x-15</=0 answer: -3</=x</=5 ok

12x^2=3x answer: x=1/4 also x = 0, (12x^2 - 3x = 0 ---> x(12x-3)=0 )

sin2x=sinx, 0</=x</=2pi answer: x=pi

no. recall that sin2x = 2(sinx)(cosx)
so
2(sinx)(cosx)-sinx=0
sinx(2cosx -1=0
sinx=0 or cosx=1/2
then x=0,pi,2pi from the first
or x = pi/3 (60º) or 5pi/3 (300º)

lx-3l<7 answer: (-oo,oo) No, -4≤x≤10

(x+1)^2(x-2)+(x+1)(x-2)^2=0
answer: x=-1,2,1/2 ok

27^(2x)=9^(x-3)answer: x=-3/2 ok

logx+log(x-3)=1 answer: x=-2,5
Your answer of x=-2 does not work in logx, you cannot take the log of a negative number. So just x=5

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