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Simplifying (z + -7)(z + -2) = 0 Reorder the terms: (-7 + z)(z + -2) = 0 Reorder the terms: (-7 + z)(-2 + z) = 0 Multiply (-7 + z) * (-2 + z) (-7(-2 + z) + z(-2 + z)) = 0 ((-2 * -7 + z * -7) + z(-2 + z)) = 0 ((14 + -7z) + z(-2 + z)) = 0 (14 + -7z + (-2 * z + z * z)) = 0 (14 + -7z + (-2z + z2)) = 0 Combine like terms: -7z + -2z = -9z (14 + -9z + z2) = 0 Solving 14 + -9z + z2 = 0 Solving for variable 'z'. Factor a trinomial. (2 + -1z)(7 + -1z) = 0Subproblem 1
Set the factor '(2 + -1z)' equal to zero and attempt to solve: Simplifying 2 + -1z = 0 Solving 2 + -1z = 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 + -1z = 0 + -2 Combine like terms: 2 + -2 = 0 0 + -1z = 0 + -2 -1z = 0 + -2 Combine like terms: 0 + -2 = -2 -1z = -2 Divide each side by '-1'. z = 2 Simplifying z = 2Subproblem 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 = {2, 7}
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