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Simplifying 2z(z + 4) + 3(z2 + -1z) = 0 Reorder the terms: 2z(4 + z) + 3(z2 + -1z) = 0 (4 * 2z + z * 2z) + 3(z2 + -1z) = 0 (8z + 2z2) + 3(z2 + -1z) = 0 Reorder the terms: 8z + 2z2 + 3(-1z + z2) = 0 8z + 2z2 + (-1z * 3 + z2 * 3) = 0 8z + 2z2 + (-3z + 3z2) = 0 Reorder the terms: 8z + -3z + 2z2 + 3z2 = 0 Combine like terms: 8z + -3z = 5z 5z + 2z2 + 3z2 = 0 Combine like terms: 2z2 + 3z2 = 5z2 5z + 5z2 = 0 Solving 5z + 5z2 = 0 Solving for variable 'z'. Factor out the Greatest Common Factor (GCF), '5z'. 5z(1 + z) = 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 '(1 + z)' equal to zero and attempt to solve: Simplifying 1 + z = 0 Solving 1 + z = 0 Move all terms containing z to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + z = 0 + -1 Combine like terms: 1 + -1 = 0 0 + z = 0 + -1 z = 0 + -1 Combine like terms: 0 + -1 = -1 z = -1 Simplifying z = -1Solution
z = {0, -1}
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