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Simplifying 4(3x + 5y + 2z) + (x + -1z) = 0 (3x * 4 + 5y * 4 + 2z * 4) + (x + -1z) = 0 (12x + 20y + 8z) + (x + -1z) = 0 Remove parenthesis around (x + -1z) 12x + 20y + 8z + x + -1z = 0 Reorder the terms: 12x + x + 20y + 8z + -1z = 0 Combine like terms: 12x + x = 13x 13x + 20y + 8z + -1z = 0 Combine like terms: 8z + -1z = 7z 13x + 20y + 7z = 0 Solving 13x + 20y + 7z = 0 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-20y' to each side of the equation. 13x + 20y + -20y + 7z = 0 + -20y Combine like terms: 20y + -20y = 0 13x + 0 + 7z = 0 + -20y 13x + 7z = 0 + -20y Remove the zero: 13x + 7z = -20y Add '-7z' to each side of the equation. 13x + 7z + -7z = -20y + -7z Combine like terms: 7z + -7z = 0 13x + 0 = -20y + -7z 13x = -20y + -7z Divide each side by '13'. x = -1.538461538y + -0.5384615385z Simplifying x = -1.538461538y + -0.5384615385z
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