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Simplifying a(x + y) + b(x + y) + c(x + y) = 0 (x * a + y * a) + b(x + y) + c(x + y) = 0 (ax + ay) + b(x + y) + c(x + y) = 0 ax + ay + (x * b + y * b) + c(x + y) = 0 ax + ay + (bx + by) + c(x + y) = 0 ax + ay + bx + by + (x * c + y * c) = 0 ax + ay + bx + by + (cx + cy) = 0 Solving ax + ay + bx + by + cx + cy = 0 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '-1bx' to each side of the equation. ax + ay + bx + by + cx + -1bx + cy = 0 + -1bx Reorder the terms: ax + ay + bx + -1bx + by + cx + cy = 0 + -1bx Combine like terms: bx + -1bx = 0 ax + ay + 0 + by + cx + cy = 0 + -1bx ax + ay + by + cx + cy = 0 + -1bx Remove the zero: ax + ay + by + cx + cy = -1bx Add '-1by' to each side of the equation. ax + ay + by + cx + -1by + cy = -1bx + -1by Reorder the terms: ax + ay + by + -1by + cx + cy = -1bx + -1by Combine like terms: by + -1by = 0 ax + ay + 0 + cx + cy = -1bx + -1by ax + ay + cx + cy = -1bx + -1by Add '-1cx' to each side of the equation. ax + ay + cx + -1cx + cy = -1bx + -1by + -1cx Combine like terms: cx + -1cx = 0 ax + ay + 0 + cy = -1bx + -1by + -1cx ax + ay + cy = -1bx + -1by + -1cx Add '-1cy' to each side of the equation. ax + ay + cy + -1cy = -1bx + -1by + -1cx + -1cy Combine like terms: cy + -1cy = 0 ax + ay + 0 = -1bx + -1by + -1cx + -1cy ax + ay = -1bx + -1by + -1cx + -1cy Reorder the terms: ax + ay + bx + by + cx + cy = -1bx + bx + -1by + by + -1cx + cx + -1cy + cy Combine like terms: -1bx + bx = 0 ax + ay + bx + by + cx + cy = 0 + -1by + by + -1cx + cx + -1cy + cy ax + ay + bx + by + cx + cy = -1by + by + -1cx + cx + -1cy + cy Combine like terms: -1by + by = 0 ax + ay + bx + by + cx + cy = 0 + -1cx + cx + -1cy + cy ax + ay + bx + by + cx + cy = -1cx + cx + -1cy + cy Combine like terms: -1cx + cx = 0 ax + ay + bx + by + cx + cy = 0 + -1cy + cy ax + ay + bx + by + cx + cy = -1cy + cy Combine like terms: -1cy + cy = 0 ax + ay + bx + by + cx + cy = 0 The solution to this equation could not be determined.
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