Summary
Highlights
Begin by finding the white centerpiece and holding it on top. Solve the white cross, ensuring the side colors line up with their respective centerpieces. If a white edge piece is on the bottom layer, align it under its matching center and rotate it 180 degrees to the top. If a piece is flipped, move it aside, rotate the top, and reinsert it correctly. If a piece is in the middle, move it to the bottom, then solve it as usual.
Learn a crucial sequence of four moves: right side up, top to the right with your right hand, right side down, top to the left with your left hand. Practice this until you can do it quickly. Then, learn the left-hand version: left side up, top to the left with your left hand, left side down, top to the right with your right hand. These sequences are vital for subsequent steps.
With the white cross solved and the cube inverted, find a white corner piece on the top layer. Identify its other two colors (e.g., green and orange) and locate the corresponding centers on the cube. Move the top layer so the corner piece is directly above its intended spot. Then, use the right-hand four-move sequence to insert it. If the piece is on the left, use the left-hand four-move sequence. If a corner is stuck on the bottom, use the moves to extract it and then solve it.
With the white side and first layer complete, turn the cube so the yellow center is on top. Find an edge piece on the top layer that does not have yellow. Match its front color with the corresponding center. Determine if it needs to go to the left or right. If to the right, move the top layer to the left, then perform the right-hand four-move sequence, followed by the left-hand four-move sequence. If to the left, move the top layer to the right, perform the left-hand four-move sequence, then the right-hand one. If an edge is already in the second layer but misplaced, insert any other piece to extract it, then solve it correctly.
Focus on creating a yellow cross on the top layer, ignoring the corners for now. If you only see a dot, turn the front face clockwise, perform the right-handed four moves, and then undo the front turn. If you have an 'L' shape, position it in the top-left and repeat the same steps. If you have a horizontal line, hold it horizontally and repeat. Once the yellow cross is formed, align as many side colors as possible with their centers. If only two align and they are adjacent, hold one at the back and one to your right. If they are opposite, perform the given algorithm from any side to get adjacent ones, then reposition and repeat.
Check if any top corners are in their correct positions (even if not oriented correctly). Find a corner with its three colors matching the surrounding centers. If one is correct, hold it in the front-right. If none are correct, perform the algorithm from any position: right-hand top turn, right side up, left-hand top turn, left side up, right-hand top turn, right side down, left-hand top turn, left side down. Repeat until all corners are in their correct positions. Once all corners are in place, turn the cube upside down so the yellow side is on the bottom.
With the cube upside down, locate a corner that needs to be oriented. Repeatedly perform the right-handed four-move sequence until that corner is correctly oriented. Once it's solved, turn only the bottom layer to bring the next unsolved corner to the front-right position (do not rotate the whole cube). Repeat the four-move sequence until it's solved. Continue this process for all remaining corners until the entire Rubik's Cube is solved.