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Simplifying (z + 6)(z + 4) = 0 Reorder the terms: (6 + z)(z + 4) = 0 Reorder the terms: (6 + z)(4 + z) = 0 Multiply (6 + z) * (4 + z) (6(4 + z) + z(4 + z)) = 0 ((4 * 6 + z * 6) + z(4 + z)) = 0 ((24 + 6z) + z(4 + z)) = 0 (24 + 6z + (4 * z + z * z)) = 0 (24 + 6z + (4z + z2)) = 0 Combine like terms: 6z + 4z = 10z (24 + 10z + z2) = 0 Solving 24 + 10z + z2 = 0 Solving for variable 'z'. Factor a trinomial. (6 + z)(4 + z) = 0Subproblem 1
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 = -6Subproblem 2
Set the factor '(4 + z)' equal to zero and attempt to solve: Simplifying 4 + z = 0 Solving 4 + z = 0 Move all terms containing z to the left, all other terms to the right. Add '-4' to each side of the equation. 4 + -4 + z = 0 + -4 Combine like terms: 4 + -4 = 0 0 + z = 0 + -4 z = 0 + -4 Combine like terms: 0 + -4 = -4 z = -4 Simplifying z = -4Solution
z = {-6, -4}
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