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Simplifying 4ax + 8ay + -12az = 0 Solving 4ax + 8ay + -12az = 0 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Factor out the Greatest Common Factor (GCF), '4a'. 4a(x + 2y + -3z) = 0 Ignore the factor 4.Subproblem 1
Set the factor 'a' equal to zero and attempt to solve: Simplifying a = 0 Solving a = 0 Move all terms containing a to the left, all other terms to the right. Simplifying a = 0Subproblem 2
Set the factor '(x + 2y + -3z)' equal to zero and attempt to solve: Simplifying x + 2y + -3z = 0 Solving x + 2y + -3z = 0 Move all terms containing a to the left, all other terms to the right. Add '-1x' to each side of the equation. x + 2y + -1x + -3z = 0 + -1x Reorder the terms: x + -1x + 2y + -3z = 0 + -1x Combine like terms: x + -1x = 0 0 + 2y + -3z = 0 + -1x 2y + -3z = 0 + -1x Remove the zero: 2y + -3z = -1x Add '-2y' to each side of the equation. 2y + -2y + -3z = -1x + -2y Combine like terms: 2y + -2y = 0 0 + -3z = -1x + -2y -3z = -1x + -2y Add '3z' to each side of the equation. -3z + 3z = -1x + -2y + 3z Combine like terms: -3z + 3z = 0 0 = -1x + -2y + 3z Simplifying 0 = -1x + -2y + 3z The solution to this equation could not be determined. This subproblem is being ignored because a solution could not be determined.Solution
a = {0}
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