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Simplifying -5z(z + 8)(z + 6) = 0 Reorder the terms: -5z(8 + z)(z + 6) = 0 Reorder the terms: -5z(8 + z)(6 + z) = 0 Multiply (8 + z) * (6 + z) -5z(8(6 + z) + z(6 + z)) = 0 -5z((6 * 8 + z * 8) + z(6 + z)) = 0 -5z((48 + 8z) + z(6 + z)) = 0 -5z(48 + 8z + (6 * z + z * z)) = 0 -5z(48 + 8z + (6z + z2)) = 0 Combine like terms: 8z + 6z = 14z -5z(48 + 14z + z2) = 0 (48 * -5z + 14z * -5z + z2 * -5z) = 0 (-240z + -70z2 + -5z3) = 0 Solving -240z + -70z2 + -5z3 = 0 Solving for variable 'z'. Factor out the Greatest Common Factor (GCF), '-5z'. -5z(48 + 14z + z2) = 0 Factor a trinomial. -5z((8 + z)(6 + 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 '(6 + z)' equal to zero and attempt to solve: Simplifying 6 + z = 0 Solving 6 + z = 0 Move all terms containing z to the left, all other terms to the right. Add '-6' to each side of the equation. 6 + -6 + z = 0 + -6 Combine like terms: 6 + -6 = 0 0 + z = 0 + -6 z = 0 + -6 Combine like terms: 0 + -6 = -6 z = -6 Simplifying z = -6Solution
z = {0, -8, -6}
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