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Simplifying (9z + 4)(2z + 1) = 0 Reorder the terms: (4 + 9z)(2z + 1) = 0 Reorder the terms: (4 + 9z)(1 + 2z) = 0 Multiply (4 + 9z) * (1 + 2z) (4(1 + 2z) + 9z * (1 + 2z)) = 0 ((1 * 4 + 2z * 4) + 9z * (1 + 2z)) = 0 ((4 + 8z) + 9z * (1 + 2z)) = 0 (4 + 8z + (1 * 9z + 2z * 9z)) = 0 (4 + 8z + (9z + 18z2)) = 0 Combine like terms: 8z + 9z = 17z (4 + 17z + 18z2) = 0 Solving 4 + 17z + 18z2 = 0 Solving for variable 'z'. Factor a trinomial. (1 + 2z)(4 + 9z) = 0Subproblem 1
Set the factor '(1 + 2z)' equal to zero and attempt to solve: Simplifying 1 + 2z = 0 Solving 1 + 2z = 0 Move all terms containing z to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + 2z = 0 + -1 Combine like terms: 1 + -1 = 0 0 + 2z = 0 + -1 2z = 0 + -1 Combine like terms: 0 + -1 = -1 2z = -1 Divide each side by '2'. z = -0.5 Simplifying z = -0.5Subproblem 2
Set the factor '(4 + 9z)' equal to zero and attempt to solve: Simplifying 4 + 9z = 0 Solving 4 + 9z = 0 Move all terms containing z to the left, all other terms to the right. Add '-4' to each side of the equation. 4 + -4 + 9z = 0 + -4 Combine like terms: 4 + -4 = 0 0 + 9z = 0 + -4 9z = 0 + -4 Combine like terms: 0 + -4 = -4 9z = -4 Divide each side by '9'. z = -0.4444444444 Simplifying z = -0.4444444444Solution
z = {-0.5, -0.4444444444}
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