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Simplifying (5z + 3)(5z + z) = 0 Reorder the terms: (3 + 5z)(5z + z) = 0 Combine like terms: 5z + z = 6z (3 + 5z)(6z) = 0 Remove parenthesis around (6z) (3 + 5z) * 6z = 0 Reorder the terms for easier multiplication: 6z(3 + 5z) = 0 (3 * 6z + 5z * 6z) = 0 (18z + 30z2) = 0 Solving 18z + 30z2 = 0 Solving for variable 'z'. Factor out the Greatest Common Factor (GCF), '6z'. 6z(3 + 5z) = 0 Ignore the factor 6.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 '(3 + 5z)' equal to zero and attempt to solve: Simplifying 3 + 5z = 0 Solving 3 + 5z = 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 + 5z = 0 + -3 Combine like terms: 3 + -3 = 0 0 + 5z = 0 + -3 5z = 0 + -3 Combine like terms: 0 + -3 = -3 5z = -3 Divide each side by '5'. z = -0.6 Simplifying z = -0.6Solution
z = {0, -0.6}
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