Solve for x:
4 (x-2) (x+6) = 4 (x+2)
Expand out terms of the left hand side:
4 x^2+16 x-48 = 4 (x+2)
Expand out terms of the right hand side:
4 x^2+16 x-48 = 4 x+8
Subtract 4 x+8 from both sides:
4 x^2+12 x-56 = 0
Divide both sides by 4:
x^2+3 x-14 = 0
Add 14 to both sides:
x^2+3 x = 14
Add 9/4 to both sides:
x^2+3 x+9/4 = 65/4
Write the left hand side as a square:
(x+3/2)^2 = 65/4
Take the square root of both sides:
x+3/2 = sqrt(65)/2 or x+3/2 = -sqrt(65)/2
Subtract 3/2 from both sides:
x = sqrt(65)/2-3/2 or x+3/2 = -sqrt(65)/2
Subtract 3/2 from both sides:
Answer: |x = sqrt(65)/2-3/2 or x = -3/2-sqrt(65)/2
