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Simplifying (9 + -1z)(2z + 3) = 0 Reorder the terms: (9 + -1z)(3 + 2z) = 0 Multiply (9 + -1z) * (3 + 2z) (9(3 + 2z) + -1z * (3 + 2z)) = 0 ((3 * 9 + 2z * 9) + -1z * (3 + 2z)) = 0 ((27 + 18z) + -1z * (3 + 2z)) = 0 (27 + 18z + (3 * -1z + 2z * -1z)) = 0 (27 + 18z + (-3z + -2z2)) = 0 Combine like terms: 18z + -3z = 15z (27 + 15z + -2z2) = 0 Solving 27 + 15z + -2z2 = 0 Solving for variable 'z'. Factor a trinomial. (9 + -1z)(3 + 2z) = 0Subproblem 1
Set the factor '(9 + -1z)' equal to zero and attempt to solve: Simplifying 9 + -1z = 0 Solving 9 + -1z = 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 + -1z = 0 + -9 Combine like terms: 9 + -9 = 0 0 + -1z = 0 + -9 -1z = 0 + -9 Combine like terms: 0 + -9 = -9 -1z = -9 Divide each side by '-1'. z = 9 Simplifying z = 9Subproblem 2
Set the factor '(3 + 2z)' equal to zero and attempt to solve: Simplifying 3 + 2z = 0 Solving 3 + 2z = 0 Move all terms containing z to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + 2z = 0 + -3 Combine like terms: 3 + -3 = 0 0 + 2z = 0 + -3 2z = 0 + -3 Combine like terms: 0 + -3 = -3 2z = -3 Divide each side by '2'. z = -1.5 Simplifying z = -1.5Solution
z = {9, -1.5}
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