x⁴+ x³- 6x²- 14x - 12 = 0

Part I: Make a list of possible rational roots.

Part II: Test the possible roots until you find one that produces a remained of 0.

Part III: Write the resulting cubic function.

Part IV: Use synthetic division to find a second root that will reduce the cubic expression to a quadratic expression.

Part V: Use the quadratic formula to find the final 2 roots.