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Simplifying (5z + -9)(2 + -1z) = 0 Reorder the terms: (-9 + 5z)(2 + -1z) = 0 Multiply (-9 + 5z) * (2 + -1z) (-9(2 + -1z) + 5z * (2 + -1z)) = 0 ((2 * -9 + -1z * -9) + 5z * (2 + -1z)) = 0 ((-18 + 9z) + 5z * (2 + -1z)) = 0 (-18 + 9z + (2 * 5z + -1z * 5z)) = 0 (-18 + 9z + (10z + -5z2)) = 0 Combine like terms: 9z + 10z = 19z (-18 + 19z + -5z2) = 0 Solving -18 + 19z + -5z2 = 0 Solving for variable 'z'. Factor a trinomial. (-2 + z)(9 + -5z) = 0Subproblem 1
Set the factor '(-2 + z)' equal to zero and attempt to solve: Simplifying -2 + z = 0 Solving -2 + z = 0 Move all terms containing z to the left, all other terms to the right. Add '2' to each side of the equation. -2 + 2 + z = 0 + 2 Combine like terms: -2 + 2 = 0 0 + z = 0 + 2 z = 0 + 2 Combine like terms: 0 + 2 = 2 z = 2 Simplifying z = 2Subproblem 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 = {2, 1.8}
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