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Simplifying (5z + -9)(7 + z) = 0 Reorder the terms: (-9 + 5z)(7 + z) = 0 Multiply (-9 + 5z) * (7 + z) (-9(7 + z) + 5z * (7 + z)) = 0 ((7 * -9 + z * -9) + 5z * (7 + z)) = 0 ((-63 + -9z) + 5z * (7 + z)) = 0 (-63 + -9z + (7 * 5z + z * 5z)) = 0 (-63 + -9z + (35z + 5z2)) = 0 Combine like terms: -9z + 35z = 26z (-63 + 26z + 5z2) = 0 Solving -63 + 26z + 5z2 = 0 Solving for variable 'z'. Factor a trinomial. (-7 + -1z)(9 + -5z) = 0Subproblem 1
Set the factor '(-7 + -1z)' equal to zero and attempt to solve: Simplifying -7 + -1z = 0 Solving -7 + -1z = 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 + -1z = 0 + 7 Combine like terms: -7 + 7 = 0 0 + -1z = 0 + 7 -1z = 0 + 7 Combine like terms: 0 + 7 = 7 -1z = 7 Divide each side by '-1'. z = -7 Simplifying z = -7Subproblem 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 = {-7, 1.8}
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