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Simplifying -40z5 + 6z4 + 4z3 = 0 Reorder the terms: 4z3 + 6z4 + -40z5 = 0 Solving 4z3 + 6z4 + -40z5 = 0 Solving for variable 'z'. Factor out the Greatest Common Factor (GCF), '2z3'. 2z3(2 + 3z + -20z2) = 0 Factor a trinomial. 2z3((2 + -5z)(1 + 4z)) = 0 Ignore the factor 2.Subproblem 1
Set the factor 'z3' equal to zero and attempt to solve: Simplifying z3 = 0 Solving z3 = 0 Move all terms containing z to the left, all other terms to the right. Simplifying z3 = 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 '(2 + -5z)' equal to zero and attempt to solve: Simplifying 2 + -5z = 0 Solving 2 + -5z = 0 Move all terms containing z to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + -5z = 0 + -2 Combine like terms: 2 + -2 = 0 0 + -5z = 0 + -2 -5z = 0 + -2 Combine like terms: 0 + -2 = -2 -5z = -2 Divide each side by '-5'. z = 0.4 Simplifying z = 0.4Subproblem 3
Set the factor '(1 + 4z)' equal to zero and attempt to solve: Simplifying 1 + 4z = 0 Solving 1 + 4z = 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 + 4z = 0 + -1 Combine like terms: 1 + -1 = 0 0 + 4z = 0 + -1 4z = 0 + -1 Combine like terms: 0 + -1 = -1 4z = -1 Divide each side by '4'. z = -0.25 Simplifying z = -0.25Solution
z = {0.4, -0.25}
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