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Simplifying 5 = z3 + 3z2 + -54z + 5 Reorder the terms: 5 = 5 + -54z + 3z2 + z3 Add '-5' to each side of the equation. 5 + -5 = 5 + -54z + 3z2 + -5 + z3 Combine like terms: 5 + -5 = 0 0 = 5 + -54z + 3z2 + -5 + z3 Reorder the terms: 0 = 5 + -5 + -54z + 3z2 + z3 Combine like terms: 5 + -5 = 0 0 = 0 + -54z + 3z2 + z3 0 = -54z + 3z2 + z3 Solving 0 = -54z + 3z2 + z3 Solving for variable 'z'. Remove the zero: 54z + -3z2 + -1z3 = -54z + 3z2 + z3 + 54z + -3z2 + -1z3 Reorder the terms: 54z + -3z2 + -1z3 = -54z + 54z + 3z2 + -3z2 + z3 + -1z3 Combine like terms: -54z + 54z = 0 54z + -3z2 + -1z3 = 0 + 3z2 + -3z2 + z3 + -1z3 54z + -3z2 + -1z3 = 3z2 + -3z2 + z3 + -1z3 Combine like terms: 3z2 + -3z2 = 0 54z + -3z2 + -1z3 = 0 + z3 + -1z3 54z + -3z2 + -1z3 = z3 + -1z3 Combine like terms: z3 + -1z3 = 0 54z + -3z2 + -1z3 = 0 Factor out the Greatest Common Factor (GCF), 'z'. z(54 + -3z + -1z2) = 0 Factor a trinomial. z((6 + -1z)(9 + z)) = 0Subproblem 1
Set the factor 'z' equal to zero and attempt to solve: Simplifying z = 0 Solving z = 0 Move all terms containing z to the left, all other terms to the right. Simplifying z = 0Subproblem 2
Set the factor '(6 + -1z)' equal to zero and attempt to solve: Simplifying 6 + -1z = 0 Solving 6 + -1z = 0 Move all terms containing z to the left, all other terms to the right. Add '-6' to each side of the equation. 6 + -6 + -1z = 0 + -6 Combine like terms: 6 + -6 = 0 0 + -1z = 0 + -6 -1z = 0 + -6 Combine like terms: 0 + -6 = -6 -1z = -6 Divide each side by '-1'. z = 6 Simplifying z = 6Subproblem 3
Set the factor '(9 + z)' equal to zero and attempt to solve: Simplifying 9 + z = 0 Solving 9 + z = 0 Move all terms containing z to the left, all other terms to the right. Add '-9' to each side of the equation. 9 + -9 + z = 0 + -9 Combine like terms: 9 + -9 = 0 0 + z = 0 + -9 z = 0 + -9 Combine like terms: 0 + -9 = -9 z = -9 Simplifying z = -9Solution
z = {0, 6, -9}
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