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Simplifying 16z4 + -60z3 + -100z2 = 0 Reorder the terms: -100z2 + -60z3 + 16z4 = 0 Solving -100z2 + -60z3 + 16z4 = 0 Solving for variable 'z'. Factor out the Greatest Common Factor (GCF), '4z2'. 4z2(-25 + -15z + 4z2) = 0 Factor a trinomial. 4z2((-5 + -4z)(5 + -1z)) = 0 Ignore the factor 4.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 '(-5 + -4z)' equal to zero and attempt to solve: Simplifying -5 + -4z = 0 Solving -5 + -4z = 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 + -4z = 0 + 5 Combine like terms: -5 + 5 = 0 0 + -4z = 0 + 5 -4z = 0 + 5 Combine like terms: 0 + 5 = 5 -4z = 5 Divide each side by '-4'. z = -1.25 Simplifying z = -1.25Subproblem 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 = {0, -1.25, 5}
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