Place all non-zero terms in the equation to one side, and set the entire equation equal to zero. The equation x^3+x^2=4x+4 would become x^3+x^2-4x-4=0.
Use factor by grouping to combine terms that have a common factor. The equation in Step 1 would be grouped as follows: (x^3+x^2)+(-4x-4)=0. Then, simplify the equation by factoring it: x^2(x+1)-4(x+1)=0.
Set each factored group equal to zero: x^2-4=0 or x+1=0.
Solve the equations in Step 3 individually. Solving the equation x+1=0 would yield x=-1. Solving the equation x^2-4=0 would yield x= +or- 2.
Plug all of the answers calculated in Step 4 back into the equation individually to test if they are solutions to the equation. The equation for the solution of -2 would be: -2^3+-2^2=4(-2)+4. Since both sides of the equation equal -4, -2 is a solution. The equation for the solution of -1 would be: (-1)^3+(-1)^2=4(-1)+4. Since both sides of the equation equal 0, -1 is a solution. The equation for the solution of 2 would be: (2)^3+(2)^2=4(2)+4. Since both sides of the equation equal 12, 2 is a solution.
List your answer as a solution set. For this problem, all of the solutions calculated in Step 4 are verifiable and, therefore, are solutions. The set notation for this problem would be {-2,-1,2}.