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Simplifying 3z8 + -9z7 + -324z6 = 0 Reorder the terms: -324z6 + -9z7 + 3z8 = 0 Solving -324z6 + -9z7 + 3z8 = 0 Solving for variable 'z'. Factor out the Greatest Common Factor (GCF), '3z6'. 3z6(-108 + -3z + z2) = 0 Factor a trinomial. 3z6((-9 + -1z)(12 + -1z)) = 0 Ignore the factor 3.Subproblem 1
Set the factor 'z6' equal to zero and attempt to solve: Simplifying z6 = 0 Solving z6 = 0 Move all terms containing z to the left, all other terms to the right. Simplifying z6 = 0 The solution to this equation could not be determined. This subproblem is being ignored because a solution could not be determined.Subproblem 2
Set the factor '(-9 + -1z)' equal to zero and attempt to solve: Simplifying -9 + -1z = 0 Solving -9 + -1z = 0 Move all terms containing z to the left, all other terms to the right. Add '9' to each side of the equation. -9 + 9 + -1z = 0 + 9 Combine like terms: -9 + 9 = 0 0 + -1z = 0 + 9 -1z = 0 + 9 Combine like terms: 0 + 9 = 9 -1z = 9 Divide each side by '-1'. z = -9 Simplifying z = -9Subproblem 3
Set the factor '(12 + -1z)' equal to zero and attempt to solve: Simplifying 12 + -1z = 0 Solving 12 + -1z = 0 Move all terms containing z to the left, all other terms to the right. Add '-12' to each side of the equation. 12 + -12 + -1z = 0 + -12 Combine like terms: 12 + -12 = 0 0 + -1z = 0 + -12 -1z = 0 + -12 Combine like terms: 0 + -12 = -12 -1z = -12 Divide each side by '-1'. z = 12 Simplifying z = 12Solution
z = {-9, 12}
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