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Simplifying 6z9 + -18z8 + -24z7 = 0 Reorder the terms: -24z7 + -18z8 + 6z9 = 0 Solving -24z7 + -18z8 + 6z9 = 0 Solving for variable 'z'. Factor out the Greatest Common Factor (GCF), '6z7'. 6z7(-4 + -3z + z2) = 0 Factor a trinomial. 6z7((-1 + -1z)(4 + -1z)) = 0 Ignore the factor 6.Subproblem 1
Set the factor 'z7' equal to zero and attempt to solve: Simplifying z7 = 0 Solving z7 = 0 Move all terms containing z to the left, all other terms to the right. Simplifying z7 = 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 '(-1 + -1z)' equal to zero and attempt to solve: Simplifying -1 + -1z = 0 Solving -1 + -1z = 0 Move all terms containing z to the left, all other terms to the right. Add '1' to each side of the equation. -1 + 1 + -1z = 0 + 1 Combine like terms: -1 + 1 = 0 0 + -1z = 0 + 1 -1z = 0 + 1 Combine like terms: 0 + 1 = 1 -1z = 1 Divide each side by '-1'. z = -1 Simplifying z = -1Subproblem 3
Set the factor '(4 + -1z)' equal to zero and attempt to solve: Simplifying 4 + -1z = 0 Solving 4 + -1z = 0 Move all terms containing z to the left, all other terms to the right. Add '-4' to each side of the equation. 4 + -4 + -1z = 0 + -4 Combine like terms: 4 + -4 = 0 0 + -1z = 0 + -4 -1z = 0 + -4 Combine like terms: 0 + -4 = -4 -1z = -4 Divide each side by '-1'. z = 4 Simplifying z = 4Solution
z = {-1, 4}
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