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Simplifying 9z(3z + 2) + z(3z + 7) = 0 Reorder the terms: 9z(2 + 3z) + z(3z + 7) = 0 (2 * 9z + 3z * 9z) + z(3z + 7) = 0 (18z + 27z2) + z(3z + 7) = 0 Reorder the terms: 18z + 27z2 + z(7 + 3z) = 0 18z + 27z2 + (7 * z + 3z * z) = 0 18z + 27z2 + (7z + 3z2) = 0 Reorder the terms: 18z + 7z + 27z2 + 3z2 = 0 Combine like terms: 18z + 7z = 25z 25z + 27z2 + 3z2 = 0 Combine like terms: 27z2 + 3z2 = 30z2 25z + 30z2 = 0 Solving 25z + 30z2 = 0 Solving for variable 'z'. Factor out the Greatest Common Factor (GCF), '5z'. 5z(5 + 6z) = 0 Ignore the factor 5.Subproblem 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 '(5 + 6z)' equal to zero and attempt to solve: Simplifying 5 + 6z = 0 Solving 5 + 6z = 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 + 6z = 0 + -5 Combine like terms: 5 + -5 = 0 0 + 6z = 0 + -5 6z = 0 + -5 Combine like terms: 0 + -5 = -5 6z = -5 Divide each side by '6'. z = -0.8333333333 Simplifying z = -0.8333333333Solution
z = {0, -0.8333333333}
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