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Simplifying (8x + 3y + -2z) + (4x + -1y + 5z) = 0 Remove parenthesis around (8x + 3y + -2z) 8x + 3y + -2z + (4x + -1y + 5z) = 0 Remove parenthesis around (4x + -1y + 5z) 8x + 3y + -2z + 4x + -1y + 5z = 0 Reorder the terms: 8x + 4x + 3y + -1y + -2z + 5z = 0 Combine like terms: 8x + 4x = 12x 12x + 3y + -1y + -2z + 5z = 0 Combine like terms: 3y + -1y = 2y 12x + 2y + -2z + 5z = 0 Combine like terms: -2z + 5z = 3z 12x + 2y + 3z = 0 Solving 12x + 2y + 3z = 0 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2y' to each side of the equation. 12x + 2y + -2y + 3z = 0 + -2y Combine like terms: 2y + -2y = 0 12x + 0 + 3z = 0 + -2y 12x + 3z = 0 + -2y Remove the zero: 12x + 3z = -2y Add '-3z' to each side of the equation. 12x + 3z + -3z = -2y + -3z Combine like terms: 3z + -3z = 0 12x + 0 = -2y + -3z 12x = -2y + -3z Divide each side by '12'. x = -0.1666666667y + -0.25z Simplifying x = -0.1666666667y + -0.25z
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