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Simplifying (4z + -5)(9 + z) = 0 Reorder the terms: (-5 + 4z)(9 + z) = 0 Multiply (-5 + 4z) * (9 + z) (-5(9 + z) + 4z * (9 + z)) = 0 ((9 * -5 + z * -5) + 4z * (9 + z)) = 0 ((-45 + -5z) + 4z * (9 + z)) = 0 (-45 + -5z + (9 * 4z + z * 4z)) = 0 (-45 + -5z + (36z + 4z2)) = 0 Combine like terms: -5z + 36z = 31z (-45 + 31z + 4z2) = 0 Solving -45 + 31z + 4z2 = 0 Solving for variable 'z'. Factor a trinomial. (-9 + -1z)(5 + -4z) = 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 '(5 + -4z)' equal to zero and attempt to solve: Simplifying 5 + -4z = 0 Solving 5 + -4z = 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 + -4z = 0 + -5 Combine like terms: 5 + -5 = 0 0 + -4z = 0 + -5 -4z = 0 + -5 Combine like terms: 0 + -5 = -5 -4z = -5 Divide each side by '-4'. z = 1.25 Simplifying z = 1.25Solution
z = {-9, 1.25}
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