1)

a^2-b^2 = (a-b)(a+b)

let a = 2x and b = root(3)

4x^2 - 3 = [(2x-root(3)][2x+root(3)]

[(2x-root(3)][2x+root(3)] = 0 means either 2x-root(3) = 0 or 2x+root(3)=0

so, either x = root(3)/2 or -root(3)/2

2)

4x + 10yz = 0 (subtract 4x from both sides)

10yz = -4x (divide both sides by 10y)

z = -4x/10y (simplify)

z = -2x/5y

3)

y^2+3yz-8z-4x = 0 (subtract y^2 and add 4x to both sides)

3yz - 8z = -y^2 + 4x (factor out z)

z(3y - 8) = -y^2 + 4x (divide by 3y-8)

z = (-y^2 + 4x)/(3y - 8)