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Simplifying (12x + -3y + 5z) + -5(-5x + 4y + -6z) = 0 Remove parenthesis around (12x + -3y + 5z) 12x + -3y + 5z + -5(-5x + 4y + -6z) = 0 12x + -3y + 5z + (-5x * -5 + 4y * -5 + -6z * -5) = 0 12x + -3y + 5z + (25x + -20y + 30z) = 0 Reorder the terms: 12x + 25x + -3y + -20y + 5z + 30z = 0 Combine like terms: 12x + 25x = 37x 37x + -3y + -20y + 5z + 30z = 0 Combine like terms: -3y + -20y = -23y 37x + -23y + 5z + 30z = 0 Combine like terms: 5z + 30z = 35z 37x + -23y + 35z = 0 Solving 37x + -23y + 35z = 0 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '23y' to each side of the equation. 37x + -23y + 23y + 35z = 0 + 23y Combine like terms: -23y + 23y = 0 37x + 0 + 35z = 0 + 23y 37x + 35z = 0 + 23y Remove the zero: 37x + 35z = 23y Add '-35z' to each side of the equation. 37x + 35z + -35z = 23y + -35z Combine like terms: 35z + -35z = 0 37x + 0 = 23y + -35z 37x = 23y + -35z Divide each side by '37'. x = 0.6216216216y + -0.9459459459z Simplifying x = 0.6216216216y + -0.9459459459z
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