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Simplifying 5z4 + -30z3 + 40z2 = 0 Reorder the terms: 40z2 + -30z3 + 5z4 = 0 Solving 40z2 + -30z3 + 5z4 = 0 Solving for variable 'z'. Factor out the Greatest Common Factor (GCF), '5z2'. 5z2(8 + -6z + z2) = 0 Factor a trinomial. 5z2((2 + -1z)(4 + -1z)) = 0 Ignore the factor 5.Subproblem 1
Set the factor 'z2' equal to zero and attempt to solve: Simplifying z2 = 0 Solving z2 = 0 Move all terms containing z to the left, all other terms to the right. Simplifying z2 = 0 Take the square root of each side: z = {0}Subproblem 2
Set the factor '(2 + -1z)' equal to zero and attempt to solve: Simplifying 2 + -1z = 0 Solving 2 + -1z = 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 + -1z = 0 + -2 Combine like terms: 2 + -2 = 0 0 + -1z = 0 + -2 -1z = 0 + -2 Combine like terms: 0 + -2 = -2 -1z = -2 Divide each side by '-1'. z = 2 Simplifying z = 2Subproblem 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 = {0, 2, 4}
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