Solve.

2x^2 = 8x

THINK IT'S:

2x^2-8x=0
2x(x-4)=0
x=0 or x= 4

That was right. I greatly appreciate your help! Thanks!!

To solve the equation 2x^2 = 8x, we can begin by rewriting it in standard quadratic form, which is ax^2 + bx + c = 0. In this case, a = 2, b = -8, and c = 0.

Step 1: Bring all the terms to one side of the equation:
2x^2 - 8x = 0

Step 2: Factorize out the common term:
2x(x - 4) = 0

Step 3: Now apply the zero product property, which states that if the product of two factors is zero, then at least one of the factors must be zero. Therefore, set each factor equal to zero:

2x = 0 or x - 4 = 0

Step 4: Solve for x in each equation:
For 2x = 0, divide both sides by 2:
x = 0

For x - 4 = 0, add 4 to both sides:
x = 4

Thus, the solutions to the equation 2x^2 = 8x are x = 0 and x = 4.