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Simplifying 3x(4x + -3y + 2z) = 0 (4x * 3x + -3y * 3x + 2z * 3x) = 0 Reorder the terms: (-9xy + 6xz + 12x2) = 0 (-9xy + 6xz + 12x2) = 0 Solving -9xy + 6xz + 12x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '3x'. 3x(-3y + 2z + 4x) = 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 + 2z + 4x)' equal to zero and attempt to solve: Simplifying -3y + 2z + 4x = 0 Reorder the terms: 4x + -3y + 2z = 0 Solving 4x + -3y + 2z = 0 Move all terms containing x to the left, all other terms to the right. Add '3y' to each side of the equation. 4x + -3y + 3y + 2z = 0 + 3y Combine like terms: -3y + 3y = 0 4x + 0 + 2z = 0 + 3y 4x + 2z = 0 + 3y Remove the zero: 4x + 2z = 3y Add '-2z' to each side of the equation. 4x + 2z + -2z = 3y + -2z Combine like terms: 2z + -2z = 0 4x + 0 = 3y + -2z 4x = 3y + -2z Divide each side by '4'. x = 0.75y + -0.5z Simplifying x = 0.75y + -0.5zSolution
x = {0, 0.75y + -0.5z}
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