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Simplifying (x + 5y + -2z + 4xy + -8yz) + (3xy + -1ax + -3y + 6z + -8yz) + -1(x + -2y + -1z + -1xy + -3yz) = 0 Reorder the terms: (x + 4xy + 5y + -8yz + -2z) + (3xy + -1ax + -3y + 6z + -8yz) + -1(x + -2y + -1z + -1xy + -3yz) = 0 Remove parenthesis around (x + 4xy + 5y + -8yz + -2z) x + 4xy + 5y + -8yz + -2z + (3xy + -1ax + -3y + 6z + -8yz) + -1(x + -2y + -1z + -1xy + -3yz) = 0 Reorder the terms: x + 4xy + 5y + -8yz + -2z + (-1ax + 3xy + -3y + -8yz + 6z) + -1(x + -2y + -1z + -1xy + -3yz) = 0 Remove parenthesis around (-1ax + 3xy + -3y + -8yz + 6z) x + 4xy + 5y + -8yz + -2z + -1ax + 3xy + -3y + -8yz + 6z + -1(x + -2y + -1z + -1xy + -3yz) = 0 Reorder the terms: x + 4xy + 5y + -8yz + -2z + -1ax + 3xy + -3y + -8yz + 6z + -1(x + -1xy + -2y + -3yz + -1z) = 0 x + 4xy + 5y + -8yz + -2z + -1ax + 3xy + -3y + -8yz + 6z + (x * -1 + -1xy * -1 + -2y * -1 + -3yz * -1 + -1z * -1) = 0 x + 4xy + 5y + -8yz + -2z + -1ax + 3xy + -3y + -8yz + 6z + (-1x + 1xy + 2y + 3yz + 1z) = 0 Reorder the terms: -1ax + x + -1x + 4xy + 3xy + 1xy + 5y + -3y + 2y + -8yz + -8yz + 3yz + -2z + 6z + 1z = 0 Combine like terms: x + -1x = 0 -1ax + 0 + 4xy + 3xy + 1xy + 5y + -3y + 2y + -8yz + -8yz + 3yz + -2z + 6z + 1z = 0 -1ax + 4xy + 3xy + 1xy + 5y + -3y + 2y + -8yz + -8yz + 3yz + -2z + 6z + 1z = 0 Combine like terms: 4xy + 3xy = 7xy -1ax + 7xy + 1xy + 5y + -3y + 2y + -8yz + -8yz + 3yz + -2z + 6z + 1z = 0 Combine like terms: 7xy + 1xy = 8xy -1ax + 8xy + 5y + -3y + 2y + -8yz + -8yz + 3yz + -2z + 6z + 1z = 0 Combine like terms: 5y + -3y = 2y -1ax + 8xy + 2y + 2y + -8yz + -8yz + 3yz + -2z + 6z + 1z = 0 Combine like terms: 2y + 2y = 4y -1ax + 8xy + 4y + -8yz + -8yz + 3yz + -2z + 6z + 1z = 0 Combine like terms: -8yz + -8yz = -16yz -1ax + 8xy + 4y + -16yz + 3yz + -2z + 6z + 1z = 0 Combine like terms: -16yz + 3yz = -13yz -1ax + 8xy + 4y + -13yz + -2z + 6z + 1z = 0 Combine like terms: -2z + 6z = 4z -1ax + 8xy + 4y + -13yz + 4z + 1z = 0 Combine like terms: 4z + 1z = 5z -1ax + 8xy + 4y + -13yz + 5z = 0 Solving -1ax + 8xy + 4y + -13yz + 5z = 0 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '-8xy' to each side of the equation. -1ax + 8xy + 4y + -13yz + -8xy + 5z = 0 + -8xy Reorder the terms: -1ax + 8xy + -8xy + 4y + -13yz + 5z = 0 + -8xy Combine like terms: 8xy + -8xy = 0 -1ax + 0 + 4y + -13yz + 5z = 0 + -8xy -1ax + 4y + -13yz + 5z = 0 + -8xy Remove the zero: -1ax + 4y + -13yz + 5z = -8xy Add '-4y' to each side of the equation. -1ax + 4y + -13yz + -4y + 5z = -8xy + -4y Reorder the terms: -1ax + 4y + -4y + -13yz + 5z = -8xy + -4y Combine like terms: 4y + -4y = 0 -1ax + 0 + -13yz + 5z = -8xy + -4y -1ax + -13yz + 5z = -8xy + -4y Add '13yz' to each side of the equation. -1ax + -13yz + 13yz + 5z = -8xy + -4y + 13yz Combine like terms: -13yz + 13yz = 0 -1ax + 0 + 5z = -8xy + -4y + 13yz -1ax + 5z = -8xy + -4y + 13yz Add '-5z' to each side of the equation. -1ax + 5z + -5z = -8xy + -4y + 13yz + -5z Combine like terms: 5z + -5z = 0 -1ax + 0 = -8xy + -4y + 13yz + -5z -1ax = -8xy + -4y + 13yz + -5z Divide each side by '-1x'. a = 8y + 4x-1y + -13x-1yz + 5x-1z Simplifying a = 8y + 4x-1y + -13x-1yz + 5x-1z Reorder the terms: a = 4x-1y + -13x-1yz + 5x-1z + 8y
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