Solve for x x^2 - 3|x - 2| - 4x = - 6

 

1. Solve for x x² - 3|x - 2| - 4x = - 6x² - 3|x - 2| - 4x = - 6 : given
   Let Y = x - 2 which gives x = Y + 2
   (Y + 2)² - 3|Y| - 4(Y + 2) = - 6 : substitute in above equation
   Y² - 3|Y| + 2 = 0
   Y² = |Y|² : note
   |Y|² - 3|Y| + 2 = 0 : rewrite equation as
   (|Y| - 2)(|Y| - 1) = 0
   |Y| = 2 , |Y| = 1 : solve for |Y|
   Y = 2, -2 , 1 , -1 : solve for Y
   x = 4 , 0 , 3 , 1 : solve for x using x = Y + 2