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Simplifying 4z3 + 15z2 + 9z = 0 Reorder the terms: 9z + 15z2 + 4z3 = 0 Solving 9z + 15z2 + 4z3 = 0 Solving for variable 'z'. Factor out the Greatest Common Factor (GCF), 'z'. z(9 + 15z + 4z2) = 0 Factor a trinomial. z((3 + z)(3 + 4z)) = 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 '(3 + z)' equal to zero and attempt to solve: Simplifying 3 + z = 0 Solving 3 + z = 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 + z = 0 + -3 Combine like terms: 3 + -3 = 0 0 + z = 0 + -3 z = 0 + -3 Combine like terms: 0 + -3 = -3 z = -3 Simplifying z = -3Subproblem 3
Set the factor '(3 + 4z)' equal to zero and attempt to solve: Simplifying 3 + 4z = 0 Solving 3 + 4z = 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 + 4z = 0 + -3 Combine like terms: 3 + -3 = 0 0 + 4z = 0 + -3 4z = 0 + -3 Combine like terms: 0 + -3 = -3 4z = -3 Divide each side by '4'. z = -0.75 Simplifying z = -0.75Solution
z = {0, -3, -0.75}
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