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Simplifying 2z9 + -24z8 + -26z7 = 0 Reorder the terms: -26z7 + -24z8 + 2z9 = 0 Solving -26z7 + -24z8 + 2z9 = 0 Solving for variable 'z'. Factor out the Greatest Common Factor (GCF), '2z7'. 2z7(-13 + -12z + z2) = 0 Factor a trinomial. 2z7((-1 + -1z)(13 + -1z)) = 0 Ignore the factor 2.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 '(13 + -1z)' equal to zero and attempt to solve: Simplifying 13 + -1z = 0 Solving 13 + -1z = 0 Move all terms containing z to the left, all other terms to the right. Add '-13' to each side of the equation. 13 + -13 + -1z = 0 + -13 Combine like terms: 13 + -13 = 0 0 + -1z = 0 + -13 -1z = 0 + -13 Combine like terms: 0 + -13 = -13 -1z = -13 Divide each side by '-1'. z = 13 Simplifying z = 13Solution
z = {-1, 13}
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