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Simplifying (z + -5)(z + -7) = 0 Reorder the terms: (-5 + z)(z + -7) = 0 Reorder the terms: (-5 + z)(-7 + z) = 0 Multiply (-5 + z) * (-7 + z) (-5(-7 + z) + z(-7 + z)) = 0 ((-7 * -5 + z * -5) + z(-7 + z)) = 0 ((35 + -5z) + z(-7 + z)) = 0 (35 + -5z + (-7 * z + z * z)) = 0 (35 + -5z + (-7z + z2)) = 0 Combine like terms: -5z + -7z = -12z (35 + -12z + z2) = 0 Solving 35 + -12z + z2 = 0 Solving for variable 'z'. Factor a trinomial. (5 + -1z)(7 + -1z) = 0Subproblem 1
Set the factor '(5 + -1z)' equal to zero and attempt to solve: Simplifying 5 + -1z = 0 Solving 5 + -1z = 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 + -1z = 0 + -5 Combine like terms: 5 + -5 = 0 0 + -1z = 0 + -5 -1z = 0 + -5 Combine like terms: 0 + -5 = -5 -1z = -5 Divide each side by '-1'. z = 5 Simplifying z = 5Subproblem 2
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 = 7Solution
z = {5, 7}
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