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Simplifying 2z6 + -4z5 + -30z4 = 0 Reorder the terms: -30z4 + -4z5 + 2z6 = 0 Solving -30z4 + -4z5 + 2z6 = 0 Solving for variable 'z'. Factor out the Greatest Common Factor (GCF), '2z4'. 2z4(-15 + -2z + z2) = 0 Factor a trinomial. 2z4((-3 + -1z)(5 + -1z)) = 0 Ignore the factor 2.Subproblem 1
Set the factor 'z4' equal to zero and attempt to solve: Simplifying z4 = 0 Solving z4 = 0 Move all terms containing z to the left, all other terms to the right. Simplifying z4 = 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 '(-3 + -1z)' equal to zero and attempt to solve: Simplifying -3 + -1z = 0 Solving -3 + -1z = 0 Move all terms containing z to the left, all other terms to the right. Add '3' to each side of the equation. -3 + 3 + -1z = 0 + 3 Combine like terms: -3 + 3 = 0 0 + -1z = 0 + 3 -1z = 0 + 3 Combine like terms: 0 + 3 = 3 -1z = 3 Divide each side by '-1'. z = -3 Simplifying z = -3Subproblem 3
Set the factor '(5 + -1z)' equal to zero and attempt to solve: Simplifying 5 + -1z = 0 Solving 5 + -1z = 0 Move all terms containing z to the left, all other terms to the right. Add '-5' to each side of the equation. 5 + -5 + -1z = 0 + -5 Combine like terms: 5 + -5 = 0 0 + -1z = 0 + -5 -1z = 0 + -5 Combine like terms: 0 + -5 = -5 -1z = -5 Divide each side by '-1'. z = 5 Simplifying z = 5Solution
z = {-3, 5}
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