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Simplifying 4z4 + -10z3 + -24z2 = 0 Reorder the terms: -24z2 + -10z3 + 4z4 = 0 Solving -24z2 + -10z3 + 4z4 = 0 Solving for variable 'z'. Factor out the Greatest Common Factor (GCF), '2z2'. 2z2(-12 + -5z + 2z2) = 0 Factor a trinomial. 2z2((-3 + -2z)(4 + -1z)) = 0 Ignore the factor 2.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 '(-3 + -2z)' equal to zero and attempt to solve: Simplifying -3 + -2z = 0 Solving -3 + -2z = 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 + -2z = 0 + 3 Combine like terms: -3 + 3 = 0 0 + -2z = 0 + 3 -2z = 0 + 3 Combine like terms: 0 + 3 = 3 -2z = 3 Divide each side by '-2'. z = -1.5 Simplifying z = -1.5Subproblem 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, -1.5, 4}
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