help!!!Maths(6Q)

Solve the following equations:
1) 6x^2+x-2=0 (by factorization)
(2x-1)(3x+2) = 0
x = 1/2 or -2/3
2) 3x^2-5x-4=0 (by formula)
x = (5+√73)/6 or (5-√73)/6
3) 4x^3-8x^2-12x=0
x^3-2x^2-3x=0
x(x^2-2x-3)=0
x(x-3)(x+1)=0
x = 0 or 3 or -1
4) 3^x=1/9^(3x-1)
3^x = 3^-3(3x-1)
x = -3(3x-1)
10x = 3
x = 3/10
5) 2^2x-2^(x+1)-8=0
2^2x - 2^(x+1) - 2^3 = 0
(2^x)^2 - 2(2^x) - 2^3 = 0
(2^x - 4)(2^x + 2) = 0
2^x = 4 or -2 (rej.)
x = 2
6) log(base10)(x-2)+log(base10)(2x-3)=1
log_10 (x-2) + log_10 (2x-3) = 1
log_10 (x-2)(2x-3) = log_10 10
2x^2 - 7x + 6 = 10
2x^2 - 7x - 4 = 0
(x-4)(2x+1)=0
x=4 or -1/2(rej. since 2(-1/2) -3 < 0)