Answer: The solution is g = 4, -8.
Step-by-step explanation: We are given to solve the following algebraic equation.
[tex]g^2+4g-32=0.[/tex]
Since the above algebraic equation is quadratic, so it will have two solutions.
The solution by the method of factorization is as follows:
[tex]g^2+4g-32=0\\\\\Rightarrow g^2+8g-4g-32=0\\\\\Rightarrow g(g+8)-4(g+8)=0\\\\\Rightarrow (g-4)(g+8)=0\\\\\Rightarrow g-4=0,~~~g+8=0\\\\\Rightarrow g=4, -8.[/tex]
Thus, the required solution is g = 4, -8.
