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Simplifying (4z + -9)(5z + -6) = 0 Reorder the terms: (-9 + 4z)(5z + -6) = 0 Reorder the terms: (-9 + 4z)(-6 + 5z) = 0 Multiply (-9 + 4z) * (-6 + 5z) (-9(-6 + 5z) + 4z * (-6 + 5z)) = 0 ((-6 * -9 + 5z * -9) + 4z * (-6 + 5z)) = 0 ((54 + -45z) + 4z * (-6 + 5z)) = 0 (54 + -45z + (-6 * 4z + 5z * 4z)) = 0 (54 + -45z + (-24z + 20z2)) = 0 Combine like terms: -45z + -24z = -69z (54 + -69z + 20z2) = 0 Solving 54 + -69z + 20z2 = 0 Solving for variable 'z'. Factor a trinomial. (6 + -5z)(9 + -4z) = 0Subproblem 1
Set the factor '(6 + -5z)' equal to zero and attempt to solve: Simplifying 6 + -5z = 0 Solving 6 + -5z = 0 Move all terms containing z to the left, all other terms to the right. Add '-6' to each side of the equation. 6 + -6 + -5z = 0 + -6 Combine like terms: 6 + -6 = 0 0 + -5z = 0 + -6 -5z = 0 + -6 Combine like terms: 0 + -6 = -6 -5z = -6 Divide each side by '-5'. z = 1.2 Simplifying z = 1.2Subproblem 2
Set the factor '(9 + -4z)' equal to zero and attempt to solve: Simplifying 9 + -4z = 0 Solving 9 + -4z = 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 + -4z = 0 + -9 Combine like terms: 9 + -9 = 0 0 + -4z = 0 + -9 -4z = 0 + -9 Combine like terms: 0 + -9 = -9 -4z = -9 Divide each side by '-4'. z = 2.25 Simplifying z = 2.25Solution
z = {1.2, 2.25}
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