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Simplifying 2(12x + 16y) + 5(3y + 4z) + 7(6x + -3y + -2z) = 0 (12x * 2 + 16y * 2) + 5(3y + 4z) + 7(6x + -3y + -2z) = 0 (24x + 32y) + 5(3y + 4z) + 7(6x + -3y + -2z) = 0 24x + 32y + (3y * 5 + 4z * 5) + 7(6x + -3y + -2z) = 0 24x + 32y + (15y + 20z) + 7(6x + -3y + -2z) = 0 24x + 32y + 15y + 20z + (6x * 7 + -3y * 7 + -2z * 7) = 0 24x + 32y + 15y + 20z + (42x + -21y + -14z) = 0 Reorder the terms: 24x + 42x + 32y + 15y + -21y + 20z + -14z = 0 Combine like terms: 24x + 42x = 66x 66x + 32y + 15y + -21y + 20z + -14z = 0 Combine like terms: 32y + 15y = 47y 66x + 47y + -21y + 20z + -14z = 0 Combine like terms: 47y + -21y = 26y 66x + 26y + 20z + -14z = 0 Combine like terms: 20z + -14z = 6z 66x + 26y + 6z = 0 Solving 66x + 26y + 6z = 0 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-26y' to each side of the equation. 66x + 26y + -26y + 6z = 0 + -26y Combine like terms: 26y + -26y = 0 66x + 0 + 6z = 0 + -26y 66x + 6z = 0 + -26y Remove the zero: 66x + 6z = -26y Add '-6z' to each side of the equation. 66x + 6z + -6z = -26y + -6z Combine like terms: 6z + -6z = 0 66x + 0 = -26y + -6z 66x = -26y + -6z Divide each side by '66'. x = -0.3939393939y + -0.09090909091z Simplifying x = -0.3939393939y + -0.09090909091z
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