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Simplifying (z + 8)(z + 12) = -3 Reorder the terms: (8 + z)(z + 12) = -3 Reorder the terms: (8 + z)(12 + z) = -3 Multiply (8 + z) * (12 + z) (8(12 + z) + z(12 + z)) = -3 ((12 * 8 + z * 8) + z(12 + z)) = -3 ((96 + 8z) + z(12 + z)) = -3 (96 + 8z + (12 * z + z * z)) = -3 (96 + 8z + (12z + z2)) = -3 Combine like terms: 8z + 12z = 20z (96 + 20z + z2) = -3 Solving 96 + 20z + z2 = -3 Solving for variable 'z'. Reorder the terms: 96 + 3 + 20z + z2 = -3 + 3 Combine like terms: 96 + 3 = 99 99 + 20z + z2 = -3 + 3 Combine like terms: -3 + 3 = 0 99 + 20z + z2 = 0 Factor a trinomial. (11 + z)(9 + z) = 0Subproblem 1
Set the factor '(11 + z)' equal to zero and attempt to solve: Simplifying 11 + z = 0 Solving 11 + z = 0 Move all terms containing z to the left, all other terms to the right. Add '-11' to each side of the equation. 11 + -11 + z = 0 + -11 Combine like terms: 11 + -11 = 0 0 + z = 0 + -11 z = 0 + -11 Combine like terms: 0 + -11 = -11 z = -11 Simplifying z = -11Subproblem 2
Set the factor '(9 + z)' equal to zero and attempt to solve: Simplifying 9 + z = 0 Solving 9 + z = 0 Move all terms containing z to the left, all other terms to the right. Add '-9' to each side of the equation. 9 + -9 + z = 0 + -9 Combine like terms: 9 + -9 = 0 0 + z = 0 + -9 z = 0 + -9 Combine like terms: 0 + -9 = -9 z = -9 Simplifying z = -9Solution
z = {-11, -9}
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