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Simplifying (2z + -5)(9 + -1z) = 0 Reorder the terms: (-5 + 2z)(9 + -1z) = 0 Multiply (-5 + 2z) * (9 + -1z) (-5(9 + -1z) + 2z * (9 + -1z)) = 0 ((9 * -5 + -1z * -5) + 2z * (9 + -1z)) = 0 ((-45 + 5z) + 2z * (9 + -1z)) = 0 (-45 + 5z + (9 * 2z + -1z * 2z)) = 0 (-45 + 5z + (18z + -2z2)) = 0 Combine like terms: 5z + 18z = 23z (-45 + 23z + -2z2) = 0 Solving -45 + 23z + -2z2 = 0 Solving for variable 'z'. Factor a trinomial. (-9 + z)(5 + -2z) = 0Subproblem 1
Set the factor '(-9 + z)' equal to zero and attempt to solve: Simplifying -9 + z = 0 Solving -9 + z = 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 + z = 0 + 9 Combine like terms: -9 + 9 = 0 0 + z = 0 + 9 z = 0 + 9 Combine like terms: 0 + 9 = 9 z = 9 Simplifying z = 9Subproblem 2
Set the factor '(5 + -2z)' equal to zero and attempt to solve: Simplifying 5 + -2z = 0 Solving 5 + -2z = 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 + -2z = 0 + -5 Combine like terms: 5 + -5 = 0 0 + -2z = 0 + -5 -2z = 0 + -5 Combine like terms: 0 + -5 = -5 -2z = -5 Divide each side by '-2'. z = 2.5 Simplifying z = 2.5Solution
z = {9, 2.5}
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