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Simplifying x3 + x2(a + b + c) + x(a * b + b * c + c * a) + a * b * c = 0 x3 + (a * x2 + b * x2 + c * x2) + x(a * b + b * c + c * a) + a * b * c = 0 x3 + (ax2 + bx2 + cx2) + x(a * b + b * c + c * a) + a * b * c = 0 Multiply a * b x3 + ax2 + bx2 + cx2 + x(ab + b * c + c * a) + a * b * c = 0 Multiply b * c x3 + ax2 + bx2 + cx2 + x(ab + bc + c * a) + a * b * c = 0 Multiply c * a x3 + ax2 + bx2 + cx2 + x(ab + bc + ac) + a * b * c = 0 Reorder the terms: x3 + ax2 + bx2 + cx2 + x(ab + ac + bc) + a * b * c = 0 x3 + ax2 + bx2 + cx2 + (ab * x + ac * x + bc * x) + a * b * c = 0 x3 + ax2 + bx2 + cx2 + (abx + acx + bcx) + a * b * c = 0 Multiply a * b x3 + ax2 + bx2 + cx2 + abx + acx + bcx + ab * c = 0 Multiply ab * c x3 + ax2 + bx2 + cx2 + abx + acx + bcx + abc = 0 Reorder the terms: abc + abx + acx + ax2 + bcx + bx2 + cx2 + x3 = 0 Solving abc + abx + acx + ax2 + bcx + bx2 + cx2 + x3 = 0 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '-1bcx' to each side of the equation. abc + abx + acx + ax2 + bcx + bx2 + cx2 + -1bcx + x3 = 0 + -1bcx Reorder the terms: abc + abx + acx + ax2 + bcx + -1bcx + bx2 + cx2 + x3 = 0 + -1bcx Combine like terms: bcx + -1bcx = 0 abc + abx + acx + ax2 + 0 + bx2 + cx2 + x3 = 0 + -1bcx abc + abx + acx + ax2 + bx2 + cx2 + x3 = 0 + -1bcx Remove the zero: abc + abx + acx + ax2 + bx2 + cx2 + x3 = -1bcx Add '-1bx2' to each side of the equation. abc + abx + acx + ax2 + bx2 + cx2 + -1bx2 + x3 = -1bcx + -1bx2 Reorder the terms: abc + abx + acx + ax2 + bx2 + -1bx2 + cx2 + x3 = -1bcx + -1bx2 Combine like terms: bx2 + -1bx2 = 0 abc + abx + acx + ax2 + 0 + cx2 + x3 = -1bcx + -1bx2 abc + abx + acx + ax2 + cx2 + x3 = -1bcx + -1bx2 Add '-1cx2' to each side of the equation. abc + abx + acx + ax2 + cx2 + -1cx2 + x3 = -1bcx + -1bx2 + -1cx2 Combine like terms: cx2 + -1cx2 = 0 abc + abx + acx + ax2 + 0 + x3 = -1bcx + -1bx2 + -1cx2 abc + abx + acx + ax2 + x3 = -1bcx + -1bx2 + -1cx2 Add '-1x3' to each side of the equation. abc + abx + acx + ax2 + x3 + -1x3 = -1bcx + -1bx2 + -1cx2 + -1x3 Combine like terms: x3 + -1x3 = 0 abc + abx + acx + ax2 + 0 = -1bcx + -1bx2 + -1cx2 + -1x3 abc + abx + acx + ax2 = -1bcx + -1bx2 + -1cx2 + -1x3 Reorder the terms: abc + abx + acx + ax2 + bcx + bx2 + cx2 + x3 = -1bcx + bcx + -1bx2 + bx2 + -1cx2 + cx2 + -1x3 + x3 Combine like terms: -1bcx + bcx = 0 abc + abx + acx + ax2 + bcx + bx2 + cx2 + x3 = 0 + -1bx2 + bx2 + -1cx2 + cx2 + -1x3 + x3 abc + abx + acx + ax2 + bcx + bx2 + cx2 + x3 = -1bx2 + bx2 + -1cx2 + cx2 + -1x3 + x3 Combine like terms: -1bx2 + bx2 = 0 abc + abx + acx + ax2 + bcx + bx2 + cx2 + x3 = 0 + -1cx2 + cx2 + -1x3 + x3 abc + abx + acx + ax2 + bcx + bx2 + cx2 + x3 = -1cx2 + cx2 + -1x3 + x3 Combine like terms: -1cx2 + cx2 = 0 abc + abx + acx + ax2 + bcx + bx2 + cx2 + x3 = 0 + -1x3 + x3 abc + abx + acx + ax2 + bcx + bx2 + cx2 + x3 = -1x3 + x3 Combine like terms: -1x3 + x3 = 0 abc + abx + acx + ax2 + bcx + bx2 + cx2 + x3 = 0 The solution to this equation could not be determined.
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