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Simplifying (2 + z)(5z + 9) = 0 Reorder the terms: (2 + z)(9 + 5z) = 0 Multiply (2 + z) * (9 + 5z) (2(9 + 5z) + z(9 + 5z)) = 0 ((9 * 2 + 5z * 2) + z(9 + 5z)) = 0 ((18 + 10z) + z(9 + 5z)) = 0 (18 + 10z + (9 * z + 5z * z)) = 0 (18 + 10z + (9z + 5z2)) = 0 Combine like terms: 10z + 9z = 19z (18 + 19z + 5z2) = 0 Solving 18 + 19z + 5z2 = 0 Solving for variable 'z'. Factor a trinomial. (2 + z)(9 + 5z) = 0Subproblem 1
Set the factor '(2 + z)' equal to zero and attempt to solve: Simplifying 2 + z = 0 Solving 2 + z = 0 Move all terms containing z to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + z = 0 + -2 Combine like terms: 2 + -2 = 0 0 + z = 0 + -2 z = 0 + -2 Combine like terms: 0 + -2 = -2 z = -2 Simplifying z = -2Subproblem 2
Set the factor '(9 + 5z)' equal to zero and attempt to solve: Simplifying 9 + 5z = 0 Solving 9 + 5z = 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 + 5z = 0 + -9 Combine like terms: 9 + -9 = 0 0 + 5z = 0 + -9 5z = 0 + -9 Combine like terms: 0 + -9 = -9 5z = -9 Divide each side by '5'. z = -1.8 Simplifying z = -1.8Solution
z = {-2, -1.8}
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