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Simplifying 6p(3x + 2y) + -1(3p + 2q)(3x + 2y) = 0 (3x * 6p + 2y * 6p) + -1(3p + 2q)(3x + 2y) = 0 (18px + 12py) + -1(3p + 2q)(3x + 2y) = 0 Multiply (3p + 2q) * (3x + 2y) 18px + 12py + -1(3p * (3x + 2y) + 2q * (3x + 2y)) = 0 18px + 12py + -1((3x * 3p + 2y * 3p) + 2q * (3x + 2y)) = 0 18px + 12py + -1((9px + 6py) + 2q * (3x + 2y)) = 0 18px + 12py + -1(9px + 6py + (3x * 2q + 2y * 2q)) = 0 18px + 12py + -1(9px + 6py + (6qx + 4qy)) = 0 18px + 12py + -1(9px + 6py + 6qx + 4qy) = 0 18px + 12py + (9px * -1 + 6py * -1 + 6qx * -1 + 4qy * -1) = 0 18px + 12py + (-9px + -6py + -6qx + -4qy) = 0 Reorder the terms: 18px + -9px + 12py + -6py + -6qx + -4qy = 0 Combine like terms: 18px + -9px = 9px 9px + 12py + -6py + -6qx + -4qy = 0 Combine like terms: 12py + -6py = 6py 9px + 6py + -6qx + -4qy = 0 Solving 9px + 6py + -6qx + -4qy = 0 Solving for variable 'p'. Move all terms containing p to the left, all other terms to the right. Add '6qx' to each side of the equation. 9px + 6py + -6qx + 6qx + -4qy = 0 + 6qx Combine like terms: -6qx + 6qx = 0 9px + 6py + 0 + -4qy = 0 + 6qx 9px + 6py + -4qy = 0 + 6qx Remove the zero: 9px + 6py + -4qy = 6qx Add '4qy' to each side of the equation. 9px + 6py + -4qy + 4qy = 6qx + 4qy Combine like terms: -4qy + 4qy = 0 9px + 6py + 0 = 6qx + 4qy 9px + 6py = 6qx + 4qy Reorder the terms: 9px + 6py + -6qx + -4qy = 6qx + -6qx + 4qy + -4qy Combine like terms: 6qx + -6qx = 0 9px + 6py + -6qx + -4qy = 0 + 4qy + -4qy 9px + 6py + -6qx + -4qy = 4qy + -4qy Combine like terms: 4qy + -4qy = 0 9px + 6py + -6qx + -4qy = 0 The solution to this equation could not be determined.
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