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Simplifying 3(5x + -2y + 4z) = 0 (5x * 3 + -2y * 3 + 4z * 3) = 0 (15x + -6y + 12z) = 0 Solving 15x + -6y + 12z = 0 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '6y' to each side of the equation. 15x + -6y + 6y + 12z = 0 + 6y Combine like terms: -6y + 6y = 0 15x + 0 + 12z = 0 + 6y 15x + 12z = 0 + 6y Remove the zero: 15x + 12z = 6y Add '-12z' to each side of the equation. 15x + 12z + -12z = 6y + -12z Combine like terms: 12z + -12z = 0 15x + 0 = 6y + -12z 15x = 6y + -12z Divide each side by '15'. x = 0.4y + -0.8z Simplifying x = 0.4y + -0.8z
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