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Simplifying -3x(6x + -3y + 4z) = 0 (6x * -3x + -3y * -3x + 4z * -3x) = 0 Reorder the terms: (9xy + -12xz + -18x2) = 0 (9xy + -12xz + -18x2) = 0 Solving 9xy + -12xz + -18x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '3x'. 3x(3y + -4z + -6x) = 0 Ignore the factor 3.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 '(3y + -4z + -6x)' equal to zero and attempt to solve: Simplifying 3y + -4z + -6x = 0 Reorder the terms: -6x + 3y + -4z = 0 Solving -6x + 3y + -4z = 0 Move all terms containing x to the left, all other terms to the right. Add '-3y' to each side of the equation. -6x + 3y + -3y + -4z = 0 + -3y Combine like terms: 3y + -3y = 0 -6x + 0 + -4z = 0 + -3y -6x + -4z = 0 + -3y Remove the zero: -6x + -4z = -3y Add '4z' to each side of the equation. -6x + -4z + 4z = -3y + 4z Combine like terms: -4z + 4z = 0 -6x + 0 = -3y + 4z -6x = -3y + 4z Divide each side by '-6'. x = 0.5y + -0.6666666667z Simplifying x = 0.5y + -0.6666666667zSolution
x = {0, 0.5y + -0.6666666667z}
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