Solve the equation. Express numbers in exact simplest form. $$ p(2 p+3)-5=2 p^{2}+4 p+2 $$ The solution set is $$ \{\square\} $$.

Question

UpStudy AI · Accepted Answer

1. Expand the left-hand side:
   $$
   p(2p+3) - 5 = 2p^2 + 3p - 5
   $$

2. Set up the equation:
   $$
   2p^2 + 3p - 5 = 2p^2 + 4p + 2
   $$

3. Subtract $$2p^2$$ from both sides:
   $$
   3p - 5 = 4p + 2
   $$

4. Subtract $$3p$$ from both sides:
   $$
   -5 = p + 2
   $$

5. Subtract 2 from both sides:
   $$
   p = -7
   $$

The solution set is $$ \{-7\} $$.
The solution is $$ p = -7 $$.

Solve the equation. Express numbers in exact simplest form. \[ p(2 p+3)-5=2 p^{2}+4 p+2 \] The solution set is \( \{\square\} \).