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Simplifying (9 + z)(5z + 8) = 0 Reorder the terms: (9 + z)(8 + 5z) = 0 Multiply (9 + z) * (8 + 5z) (9(8 + 5z) + z(8 + 5z)) = 0 ((8 * 9 + 5z * 9) + z(8 + 5z)) = 0 ((72 + 45z) + z(8 + 5z)) = 0 (72 + 45z + (8 * z + 5z * z)) = 0 (72 + 45z + (8z + 5z2)) = 0 Combine like terms: 45z + 8z = 53z (72 + 53z + 5z2) = 0 Solving 72 + 53z + 5z2 = 0 Solving for variable 'z'. Factor a trinomial. (9 + z)(8 + 5z) = 0Subproblem 1
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 = -9Subproblem 2
Set the factor '(8 + 5z)' equal to zero and attempt to solve: Simplifying 8 + 5z = 0 Solving 8 + 5z = 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 + 5z = 0 + -8 Combine like terms: 8 + -8 = 0 0 + 5z = 0 + -8 5z = 0 + -8 Combine like terms: 0 + -8 = -8 5z = -8 Divide each side by '5'. z = -1.6 Simplifying z = -1.6Solution
z = {-9, -1.6}
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