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Simplifying 0 = 3z(8 + -5z) 0 = (8 * 3z + -5z * 3z) 0 = (24z + -15z2) Solving 0 = 24z + -15z2 Solving for variable 'z'. Remove the zero: -24z + 15z2 = 24z + -15z2 + -24z + 15z2 Reorder the terms: -24z + 15z2 = 24z + -24z + -15z2 + 15z2 Combine like terms: 24z + -24z = 0 -24z + 15z2 = 0 + -15z2 + 15z2 -24z + 15z2 = -15z2 + 15z2 Combine like terms: -15z2 + 15z2 = 0 -24z + 15z2 = 0 Factor out the Greatest Common Factor (GCF), '3z'. 3z(-8 + 5z) = 0 Ignore the factor 3.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 '(-8 + 5z)' equal to zero and attempt to solve: Simplifying -8 + 5z = 0 Solving -8 + 5z = 0 Move all terms containing z to the left, all other terms to the right. Add '8' to each side of the equation. -8 + 8 + 5z = 0 + 8 Combine like terms: -8 + 8 = 0 0 + 5z = 0 + 8 5z = 0 + 8 Combine like terms: 0 + 8 = 8 5z = 8 Divide each side by '5'. z = 1.6 Simplifying z = 1.6Solution
z = {0, 1.6}
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