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Simplifying (9 + z)(3z + -5) = 0 Reorder the terms: (9 + z)(-5 + 3z) = 0 Multiply (9 + z) * (-5 + 3z) (9(-5 + 3z) + z(-5 + 3z)) = 0 ((-5 * 9 + 3z * 9) + z(-5 + 3z)) = 0 ((-45 + 27z) + z(-5 + 3z)) = 0 (-45 + 27z + (-5 * z + 3z * z)) = 0 (-45 + 27z + (-5z + 3z2)) = 0 Combine like terms: 27z + -5z = 22z (-45 + 22z + 3z2) = 0 Solving -45 + 22z + 3z2 = 0 Solving for variable 'z'. Factor a trinomial. (-9 + -1z)(5 + -3z) = 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 + -3z)' equal to zero and attempt to solve: Simplifying 5 + -3z = 0 Solving 5 + -3z = 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 + -3z = 0 + -5 Combine like terms: 5 + -5 = 0 0 + -3z = 0 + -5 -3z = 0 + -5 Combine like terms: 0 + -5 = -5 -3z = -5 Divide each side by '-3'. z = 1.666666667 Simplifying z = 1.666666667Solution
z = {-9, 1.666666667}
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