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Simplifying 4x + 8y + -12z + -15y + -10x + -5z = 0 Reorder the terms: 4x + -10x + 8y + -15y + -12z + -5z = 0 Combine like terms: 4x + -10x = -6x -6x + 8y + -15y + -12z + -5z = 0 Combine like terms: 8y + -15y = -7y -6x + -7y + -12z + -5z = 0 Combine like terms: -12z + -5z = -17z -6x + -7y + -17z = 0 Solving -6x + -7y + -17z = 0 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '7y' to each side of the equation. -6x + -7y + 7y + -17z = 0 + 7y Combine like terms: -7y + 7y = 0 -6x + 0 + -17z = 0 + 7y -6x + -17z = 0 + 7y Remove the zero: -6x + -17z = 7y Add '17z' to each side of the equation. -6x + -17z + 17z = 7y + 17z Combine like terms: -17z + 17z = 0 -6x + 0 = 7y + 17z -6x = 7y + 17z Divide each side by '-6'. x = -1.166666667y + -2.833333333z Simplifying x = -1.166666667y + -2.833333333z
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