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Simplifying 5z(z + 1)(z + 8) = 0 Reorder the terms: 5z(1 + z)(z + 8) = 0 Reorder the terms: 5z(1 + z)(8 + z) = 0 Multiply (1 + z) * (8 + z) 5z(1(8 + z) + z(8 + z)) = 0 5z((8 * 1 + z * 1) + z(8 + z)) = 0 5z((8 + 1z) + z(8 + z)) = 0 5z(8 + 1z + (8 * z + z * z)) = 0 5z(8 + 1z + (8z + z2)) = 0 Combine like terms: 1z + 8z = 9z 5z(8 + 9z + z2) = 0 (8 * 5z + 9z * 5z + z2 * 5z) = 0 (40z + 45z2 + 5z3) = 0 Solving 40z + 45z2 + 5z3 = 0 Solving for variable 'z'. Factor out the Greatest Common Factor (GCF), '5z'. 5z(8 + 9z + z2) = 0 Factor a trinomial. 5z((8 + z)(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 '(8 + z)' equal to zero and attempt to solve: Simplifying 8 + z = 0 Solving 8 + z = 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 + z = 0 + -8 Combine like terms: 8 + -8 = 0 0 + z = 0 + -8 z = 0 + -8 Combine like terms: 0 + -8 = -8 z = -8 Simplifying z = -8Subproblem 3
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, -8, -1}
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