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

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

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

Answer：
x2 - 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.