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Simplifying z3 + 12z2 + 35z = 0 Reorder the terms: 35z + 12z2 + z3 = 0 Solving 35z + 12z2 + z3 = 0 Solving for variable 'z'. Factor out the Greatest Common Factor (GCF), 'z'. z(35 + 12z + z2) = 0 Factor a trinomial. z((7 + z)(5 + 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 '(7 + z)' equal to zero and attempt to solve: Simplifying 7 + z = 0 Solving 7 + z = 0 Move all terms containing z to the left, all other terms to the right. Add '-7' to each side of the equation. 7 + -7 + z = 0 + -7 Combine like terms: 7 + -7 = 0 0 + z = 0 + -7 z = 0 + -7 Combine like terms: 0 + -7 = -7 z = -7 Simplifying z = -7Subproblem 3
Set the factor '(5 + z)' equal to zero and attempt to solve: Simplifying 5 + z = 0 Solving 5 + z = 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 + z = 0 + -5 Combine like terms: 5 + -5 = 0 0 + z = 0 + -5 z = 0 + -5 Combine like terms: 0 + -5 = -5 z = -5 Simplifying z = -5Solution
z = {0, -7, -5}
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