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Simplifying 5z7 + -5z6 + -910z5 = 0 Reorder the terms: -910z5 + -5z6 + 5z7 = 0 Solving -910z5 + -5z6 + 5z7 = 0 Solving for variable 'z'. Factor out the Greatest Common Factor (GCF), '5z5'. 5z5(-182 + -1z + z2) = 0 Factor a trinomial. 5z5((-13 + -1z)(14 + -1z)) = 0 Ignore the factor 5.Subproblem 1
Set the factor 'z5' equal to zero and attempt to solve: Simplifying z5 = 0 Solving z5 = 0 Move all terms containing z to the left, all other terms to the right. Simplifying z5 = 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 '(-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 = -13Subproblem 3
Set the factor '(14 + -1z)' equal to zero and attempt to solve: Simplifying 14 + -1z = 0 Solving 14 + -1z = 0 Move all terms containing z to the left, all other terms to the right. Add '-14' to each side of the equation. 14 + -14 + -1z = 0 + -14 Combine like terms: 14 + -14 = 0 0 + -1z = 0 + -14 -1z = 0 + -14 Combine like terms: 0 + -14 = -14 -1z = -14 Divide each side by '-1'. z = 14 Simplifying z = 14Solution
z = {-13, 14}
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