Solve for x, 8x² + 64x = 0

Solution:

In the given equation:

8x² + 64x = 0.

We will use the zero product rule to solve the equation.

Step 1: Take out the common factors.

⇒ 8x (x + 8) = 0

As we can see that the product of 8x and (x + 8) is equal to zero.

Therefore,

the zero product rule says that the product of factors is zero if and only one or more factors is zero.

Step 2: Consider both the factors equal to zero.

⇒ 8x = 0, we get x = 0

⇒ and x + 8 = 0,

we get x = - 8

Hence, the values of x which satisfies the equation 8x² + 64x = 0 are x = 0 and - 8.

Solve for x, 8x² + 64x = 0

Summary:

The equation 8x²+ 64x = 0 has two solutions x = 0, and - 8.