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Simplifying (z + -1)(z + -7) = 0 Reorder the terms: (-1 + z)(z + -7) = 0 Reorder the terms: (-1 + z)(-7 + z) = 0 Multiply (-1 + z) * (-7 + z) (-1(-7 + z) + z(-7 + z)) = 0 ((-7 * -1 + z * -1) + z(-7 + z)) = 0 ((7 + -1z) + z(-7 + z)) = 0 (7 + -1z + (-7 * z + z * z)) = 0 (7 + -1z + (-7z + z2)) = 0 Combine like terms: -1z + -7z = -8z (7 + -8z + z2) = 0 Solving 7 + -8z + z2 = 0 Solving for variable 'z'. Factor a trinomial. (1 + -1z)(7 + -1z) = 0Subproblem 1
Set the factor '(1 + -1z)' equal to zero and attempt to solve: Simplifying 1 + -1z = 0 Solving 1 + -1z = 0 Move all terms containing z to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + -1z = 0 + -1 Combine like terms: 1 + -1 = 0 0 + -1z = 0 + -1 -1z = 0 + -1 Combine like terms: 0 + -1 = -1 -1z = -1 Divide each side by '-1'. z = 1 Simplifying z = 1Subproblem 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 = {1, 7}
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