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Simplifying (5 + z)(5z + -9) = 0 Reorder the terms: (5 + z)(-9 + 5z) = 0 Multiply (5 + z) * (-9 + 5z) (5(-9 + 5z) + z(-9 + 5z)) = 0 ((-9 * 5 + 5z * 5) + z(-9 + 5z)) = 0 ((-45 + 25z) + z(-9 + 5z)) = 0 (-45 + 25z + (-9 * z + 5z * z)) = 0 (-45 + 25z + (-9z + 5z2)) = 0 Combine like terms: 25z + -9z = 16z (-45 + 16z + 5z2) = 0 Solving -45 + 16z + 5z2 = 0 Solving for variable 'z'. Factor a trinomial. (-5 + -1z)(9 + -5z) = 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 + -5z)' equal to zero and attempt to solve: Simplifying 9 + -5z = 0 Solving 9 + -5z = 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 + -5z = 0 + -9 Combine like terms: 9 + -9 = 0 0 + -5z = 0 + -9 -5z = 0 + -9 Combine like terms: 0 + -9 = -9 -5z = -9 Divide each side by '-5'. z = 1.8 Simplifying z = 1.8Solution
z = {-5, 1.8}
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