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Simplifying 8x(x + 3y + 4z) = 0 (x * 8x + 3y * 8x + 4z * 8x) = 0 Reorder the terms: (24xy + 32xz + 8x2) = 0 (24xy + 32xz + 8x2) = 0 Solving 24xy + 32xz + 8x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '8x'. 8x(3y + 4z + x) = 0 Ignore the factor 8.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 + x)' equal to zero and attempt to solve: Simplifying 3y + 4z + x = 0 Reorder the terms: x + 3y + 4z = 0 Solving x + 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. x + 3y + -3y + 4z = 0 + -3y Combine like terms: 3y + -3y = 0 x + 0 + 4z = 0 + -3y x + 4z = 0 + -3y Remove the zero: x + 4z = -3y Add '-4z' to each side of the equation. x + 4z + -4z = -3y + -4z Combine like terms: 4z + -4z = 0 x + 0 = -3y + -4z x = -3y + -4z Simplifying x = -3y + -4zSolution
x = {0, -3y + -4z}
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