First, subtract #color(red)(y)# and #color(blue)(36)# from each side of the equation to form a standard quadratic equation:
#2y^2 - color(red)(y) - color(blue)(36) = y - color(red)(y) + 36 - color(blue)(36)#
#2y^2 - y - 36 = 0 + 0#
#2y^2 - y - 36 = 0#
Next, factor the quadratic as:
#(2y - 9)(y + 4) = 0#
Now solve each term on the left for #0#:
Solution 1)
#2y - 9 = 0#
#2y - 9 + color(red)(9) = 0 + color(red)(9)#
#2y - 0 = 9#
#2y = 9#
#(2y)/color(red)(2) = 9/color(red)(2)#
#(color(red)(cancel(color(black)(2)))y)/cancel(color(red)(2)) = 9/2#
#y = 9/2#
Solution)
#y + 4 = 0#
#y + 4 - color(red)(4) = 0 - color(red)(4)#
#y + 0 = -4#
#y = -4#
The solution: #y = 9/2#; #y = -4#
