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Simplifying (5z + 7)(9 + -1z) = 0 Reorder the terms: (7 + 5z)(9 + -1z) = 0 Multiply (7 + 5z) * (9 + -1z) (7(9 + -1z) + 5z * (9 + -1z)) = 0 ((9 * 7 + -1z * 7) + 5z * (9 + -1z)) = 0 ((63 + -7z) + 5z * (9 + -1z)) = 0 (63 + -7z + (9 * 5z + -1z * 5z)) = 0 (63 + -7z + (45z + -5z2)) = 0 Combine like terms: -7z + 45z = 38z (63 + 38z + -5z2) = 0 Solving 63 + 38z + -5z2 = 0 Solving for variable 'z'. Factor a trinomial. (9 + -1z)(7 + 5z) = 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 '(7 + 5z)' equal to zero and attempt to solve: Simplifying 7 + 5z = 0 Solving 7 + 5z = 0 Move all terms containing z to the left, all other terms to the right. Add '-7' to each side of the equation. 7 + -7 + 5z = 0 + -7 Combine like terms: 7 + -7 = 0 0 + 5z = 0 + -7 5z = 0 + -7 Combine like terms: 0 + -7 = -7 5z = -7 Divide each side by '5'. z = -1.4 Simplifying z = -1.4Solution
z = {9, -1.4}
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