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Simplifying (a + b + c) * x3 = 0 Reorder the terms for easier multiplication: x3(a + b + c) = 0 (a * x3 + b * x3 + c * x3) = 0 (ax3 + bx3 + cx3) = 0 Solving ax3 + bx3 + cx3 = 0 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '-1bx3' to each side of the equation. ax3 + bx3 + -1bx3 + cx3 = 0 + -1bx3 Combine like terms: bx3 + -1bx3 = 0 ax3 + 0 + cx3 = 0 + -1bx3 ax3 + cx3 = 0 + -1bx3 Remove the zero: ax3 + cx3 = -1bx3 Add '-1cx3' to each side of the equation. ax3 + cx3 + -1cx3 = -1bx3 + -1cx3 Combine like terms: cx3 + -1cx3 = 0 ax3 + 0 = -1bx3 + -1cx3 ax3 = -1bx3 + -1cx3 Divide each side by 'x3'. a = -1b + -1c Simplifying a = -1b + -1c
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