I cannot figure out how to apply Langrarian to solve this...I get lost on solving for zero, like the sample below.

Example Maximize: U = Q 0.6 Q,0.4 P1 = $15 P2= $20 Y = $300 Subject to : P,Q1 + P2Q2 = Y Set Up the Lagrangian L = Q,0.6 Q20.4 - 1(15Q, + 20Q2 - 300) OL/2Q1 = 0.6Q,-04Q204 - 15 =0 OL/8Q2 = 0.4Q,0.6Q2-0.6 - 120=0 OL/OX = 15Q1 + 20Q2 - 30 = 0 0.6Q1-0.4Q,0.4 X15 ---- = 0 0.4Q 0.6Q,-0.6 120 3Q2 15 ------ ---- 2Q1 20 Q2 = 0.5Q1 L/2X = 15Q1 + 20Q2 - 300 = 0 15Q1 + 20Q2 = 300 Substitute Q2 = 0.5Q, 15Q1 + 20(0.5Q1 ) = 300 25Q1 = 300 Q1* = 12 Q,* = 6