Solve the equation by factoring. Check your answer.
4x^2=8x
To solve the equation by factoring, we want to set the equation equal to zero. Thus, we have:
4x^2 - 8x = 0.
Next, we can factor out a common factor of 4x:
4x(x - 2) = 0.
Now, we can set each factor equal to zero and solve for x:
4x = 0 OR x - 2 = 0.
If 4x = 0, then x = 0.
If x - 2 = 0, then x = 2.
To check our answer, we substitute the values of x back into the original equation:
4(0)^2 = 8(0)
0 = 0
This equation holds true when x = 0.
4(2)^2 = 8(2)
16 = 16
This equation also holds true when x = 2.
Therefore, our solution is x = 0 or x = 2.