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Simplifying 3(2x + 4y + -2z) + 7(x + y + -4z) = 0 (2x * 3 + 4y * 3 + -2z * 3) + 7(x + y + -4z) = 0 (6x + 12y + -6z) + 7(x + y + -4z) = 0 6x + 12y + -6z + (x * 7 + y * 7 + -4z * 7) = 0 6x + 12y + -6z + (7x + 7y + -28z) = 0 Reorder the terms: 6x + 7x + 12y + 7y + -6z + -28z = 0 Combine like terms: 6x + 7x = 13x 13x + 12y + 7y + -6z + -28z = 0 Combine like terms: 12y + 7y = 19y 13x + 19y + -6z + -28z = 0 Combine like terms: -6z + -28z = -34z 13x + 19y + -34z = 0 Solving 13x + 19y + -34z = 0 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-19y' to each side of the equation. 13x + 19y + -19y + -34z = 0 + -19y Combine like terms: 19y + -19y = 0 13x + 0 + -34z = 0 + -19y 13x + -34z = 0 + -19y Remove the zero: 13x + -34z = -19y Add '34z' to each side of the equation. 13x + -34z + 34z = -19y + 34z Combine like terms: -34z + 34z = 0 13x + 0 = -19y + 34z 13x = -19y + 34z Divide each side by '13'. x = -1.461538462y + 2.615384615z Simplifying x = -1.461538462y + 2.615384615z
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