We have rewritten the left-hand side as a product of three factors. Now, we will apply the Zero Product Property to solve the equation.
Note that since 2≠0, we will not consider it when applying the property.
From Equation (I), we found that one solution is x= 23. To find other solutions, we will solve Equation (II). Note that since this is a quadratic equation, we will use the Quadratic Formula.
ax^2+bx+c=0 ⇔ x=- b±sqrt(b^2-4ac)/2a
To do so, we first need to identify a, b, and c.
9x^2+ 6x+ 4=0
We can see above that a= 9, b= 6, and c= 4. Let's substitute these values into the formula and solve for x.
We found that the solutions for the quadratic equation are x= - 1± isqrt(3)3. Notice that they are not real solutions, thus the only real solution is 23.
Real solution
x=2/3
