2p^2 + 8p = -3

To solve the equation 2p^2 + 8p = -3, you can follow these steps:

Step 1: Rewrite the equation in standard quadratic form, which is ax^2 + bx + c = 0. In this case, rearrange the equation to have all terms on one side:
2p^2 + 8p + 3 = 0

Step 2: Factor the quadratic expression. In this case, the quadratic expression can be factored into two binomials since the coefficient of the term p^2 is 2:
(2p + 1)(p + 3) = 0

Step 3: Set each factor equal to zero and solve for p:
2p + 1 = 0 or p + 3 = 0

For the first factor, subtract 1 from both sides and divide by 2:
2p = -1
p = -1/2

For the second factor, subtract 3 from both sides:
p = -3

So the solutions to the equation 2p^2 + 8p = -3 are p = -1/2 and p = -3.