2x(x+3) = 0

Is there a way to solve that using the below methods?

Substitute zero for f(x) and find the roots of the resulting equation, or graph the function and determine the x-intercepts of the graph.

Finding the roots of a single variable equation may involve factoring. Except in the case of a linear equation, set the equation to zero before factoring. Recall the following techniques for factoring: common factors, difference of two squares, trinomials in the form x^2+bx+c=0, and trinomials of the form ax^2+bx+c=0

2x(x+3)=0 then

either 2x=0 or x+3=0 so
x=0; or -3

Thank you so much bobpursley, I was so confused on how to do this, you are a lifesaver!

Yes, there is a way to solve the equation 2x(x+3) = 0 using the methods you mentioned.

First, let's use the method of substituting zero for f(x) and finding the roots of the resulting equation.

Substituting zero for f(x), we get:

2x(x + 3) = 0
2x * 0 = 0

Since any number multiplied by zero equals zero, this equation is satisfied when either 2x = 0 or (x + 3) = 0.

For 2x = 0, divide both sides by 2 to isolate x:

x = 0

For (x + 3) = 0, subtract 3 from both sides to isolate x:

x = -3

Therefore, we have found two possible solutions: x = 0 and x = -3.

Now, let's use the method of graphing the function and determining the x-intercepts.

To do this, we can plot the function y = 2x(x + 3) on a graph and identify the points where the graph intersects the x-axis, which represent the x-intercepts.

The equation 2x(x + 3) = 0 represents a parabola that opens upwards due to the positive coefficient of the leading term (2x^2). This means that the graph will intersect the x-axis at two points.

By factoring the equation, we can rewrite it as:

2x(x + 3) = 0
2x = 0 or (x + 3) = 0

From this, we get the same solutions we found previously: x = 0 and x = -3.

So, the x-intercepts of the graph of y = 2x(x + 3) are x = 0 and x = -3.

In conclusion, both methods yield the same solutions, which are x = 0 and x = -3. We can find the roots by either substituting zero for f(x) and solving the resulting equation or by graphing the function and identifying the x-intercepts.