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Simplifying (5 + -1z)(2z + 9) = 0 Reorder the terms: (5 + -1z)(9 + 2z) = 0 Multiply (5 + -1z) * (9 + 2z) (5(9 + 2z) + -1z * (9 + 2z)) = 0 ((9 * 5 + 2z * 5) + -1z * (9 + 2z)) = 0 ((45 + 10z) + -1z * (9 + 2z)) = 0 (45 + 10z + (9 * -1z + 2z * -1z)) = 0 (45 + 10z + (-9z + -2z2)) = 0 Combine like terms: 10z + -9z = 1z (45 + 1z + -2z2) = 0 Solving 45 + 1z + -2z2 = 0 Solving for variable 'z'. Factor a trinomial. (5 + -1z)(9 + 2z) = 0Subproblem 1
Set the factor '(5 + -1z)' equal to zero and attempt to solve: Simplifying 5 + -1z = 0 Solving 5 + -1z = 0 Move all terms containing z to the left, all other terms to the right. Add '-5' to each side of the equation. 5 + -5 + -1z = 0 + -5 Combine like terms: 5 + -5 = 0 0 + -1z = 0 + -5 -1z = 0 + -5 Combine like terms: 0 + -5 = -5 -1z = -5 Divide each side by '-1'. z = 5 Simplifying z = 5Subproblem 2
Set the factor '(9 + 2z)' equal to zero and attempt to solve: Simplifying 9 + 2z = 0 Solving 9 + 2z = 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 + 2z = 0 + -9 Combine like terms: 9 + -9 = 0 0 + 2z = 0 + -9 2z = 0 + -9 Combine like terms: 0 + -9 = -9 2z = -9 Divide each side by '2'. z = -4.5 Simplifying z = -4.5Solution
z = {5, -4.5}
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