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Simplifying -4z(z + 6)(z + -8) = 0 Reorder the terms: -4z(6 + z)(z + -8) = 0 Reorder the terms: -4z(6 + z)(-8 + z) = 0 Multiply (6 + z) * (-8 + z) -4z(6(-8 + z) + z(-8 + z)) = 0 -4z((-8 * 6 + z * 6) + z(-8 + z)) = 0 -4z((-48 + 6z) + z(-8 + z)) = 0 -4z(-48 + 6z + (-8 * z + z * z)) = 0 -4z(-48 + 6z + (-8z + z2)) = 0 Combine like terms: 6z + -8z = -2z -4z(-48 + -2z + z2) = 0 (-48 * -4z + -2z * -4z + z2 * -4z) = 0 (192z + 8z2 + -4z3) = 0 Solving 192z + 8z2 + -4z3 = 0 Solving for variable 'z'. Factor out the Greatest Common Factor (GCF), '4z'. 4z(48 + 2z + -1z2) = 0 Factor a trinomial. 4z((8 + -1z)(6 + z)) = 0 Ignore the factor 4.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 + -1z)' equal to zero and attempt to solve: Simplifying 8 + -1z = 0 Solving 8 + -1z = 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 + -1z = 0 + -8 Combine like terms: 8 + -8 = 0 0 + -1z = 0 + -8 -1z = 0 + -8 Combine like terms: 0 + -8 = -8 -1z = -8 Divide each side by '-1'. 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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