Nico solved the equation: 4x+6=3x-x2. His work is below.
4x+6=3x-x2
x2+4x+6=3x
x2+7x+6=0
(x+6)(x+1)=0
x+6=0 or x+1=0
x= -6 or x= -1
Nico’s teacher says his answers {-6, -1} are wrong. Explain why Nico’s answer of {-6} cannot be a solution to the equation. Then, describe the process he could follow to solve the equation 4x+6=3x-x2. Find the actual solution(s).
