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Simplifying 6x(x + 2y + 3z) = 0 (x * 6x + 2y * 6x + 3z * 6x) = 0 Reorder the terms: (12xy + 18xz + 6x2) = 0 (12xy + 18xz + 6x2) = 0 Solving 12xy + 18xz + 6x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '6x'. 6x(2y + 3z + x) = 0 Ignore the factor 6.Subproblem 1
Set the factor 'x' equal to zero and attempt to solve: Simplifying x = 0 Solving x = 0 Move all terms containing x to the left, all other terms to the right. Simplifying x = 0Subproblem 2
Set the factor '(2y + 3z + x)' equal to zero and attempt to solve: Simplifying 2y + 3z + x = 0 Reorder the terms: x + 2y + 3z = 0 Solving x + 2y + 3z = 0 Move all terms containing x to the left, all other terms to the right. Add '-2y' to each side of the equation. x + 2y + -2y + 3z = 0 + -2y Combine like terms: 2y + -2y = 0 x + 0 + 3z = 0 + -2y x + 3z = 0 + -2y Remove the zero: x + 3z = -2y Add '-3z' to each side of the equation. x + 3z + -3z = -2y + -3z Combine like terms: 3z + -3z = 0 x + 0 = -2y + -3z x = -2y + -3z Simplifying x = -2y + -3zSolution
x = {0, -2y + -3z}
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