Quadratic Equations

Find the condition that in the equations $$\displaystyle ax^{3}+bx+c=0$$ and $$dx^{2}+b'x+c'=0$$
Solved :
Step $$1: x^{2} - 3x^{2}y^{2} + x^{2}y^{2} - 2x^{2} - 3y^{2} + 12x^{2}y^{2}$$
Step $$2 : (x^{2} - 2x^{2}) + (-3x^{2}y^{2} + x^{2}y^{2} + 12x^{2}y^{2}) - 3y^{2}$$
Step $$3 : (-x^{2} + 10x^{2}y^{2} - 3y^{2})$$
Are the above given steps showing simplification of algebraic expression
$$x^{2} (1 - 3y^{2}) + (xy^{2} - 2x) - 3y(y - 4x^{2}y)$$?
If the graph of a quadratic polynomial $$ax^2+bx+c$$ touches the X-axis at two points (as shown above), which of the following statements is correct?
The number of solutions of the equation
$$3\sin^{2}x-7\sin x+2=0$$
in the interval $$[0, 5\pi]$$ is:-