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Simplifying 9x(2 + 8y + -5z) + x(8y + 3 + -10z) = 0 (2 * 9x + 8y * 9x + -5z * 9x) + x(8y + 3 + -10z) = 0 (18x + 72xy + -45xz) + x(8y + 3 + -10z) = 0 Reorder the terms: 18x + 72xy + -45xz + x(3 + 8y + -10z) = 0 18x + 72xy + -45xz + (3 * x + 8y * x + -10z * x) = 0 18x + 72xy + -45xz + (3x + 8xy + -10xz) = 0 Reorder the terms: 18x + 3x + 72xy + 8xy + -45xz + -10xz = 0 Combine like terms: 18x + 3x = 21x 21x + 72xy + 8xy + -45xz + -10xz = 0 Combine like terms: 72xy + 8xy = 80xy 21x + 80xy + -45xz + -10xz = 0 Combine like terms: -45xz + -10xz = -55xz 21x + 80xy + -55xz = 0 Solving 21x + 80xy + -55xz = 0 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Factor out the Greatest Common Factor (GCF), 'x'. x(21 + 80y + -55z) = 0Subproblem 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 '(21 + 80y + -55z)' equal to zero and attempt to solve: Simplifying 21 + 80y + -55z = 0 Solving 21 + 80y + -55z = 0 Move all terms containing x to the left, all other terms to the right. Add '-21' to each side of the equation. 21 + 80y + -21 + -55z = 0 + -21 Reorder the terms: 21 + -21 + 80y + -55z = 0 + -21 Combine like terms: 21 + -21 = 0 0 + 80y + -55z = 0 + -21 80y + -55z = 0 + -21 Combine like terms: 0 + -21 = -21 80y + -55z = -21 Add '-80y' to each side of the equation. 80y + -80y + -55z = -21 + -80y Combine like terms: 80y + -80y = 0 0 + -55z = -21 + -80y -55z = -21 + -80y Add '55z' to each side of the equation. -55z + 55z = -21 + -80y + 55z Combine like terms: -55z + 55z = 0 0 = -21 + -80y + 55z Simplifying 0 = -21 + -80y + 55z The solution to this equation could not be determined. This subproblem is being ignored because a solution could not be determined.Solution
x = {0}
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