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Simplifying (z + -3)(z + -7) = 0 Reorder the terms: (-3 + z)(z + -7) = 0 Reorder the terms: (-3 + z)(-7 + z) = 0 Multiply (-3 + z) * (-7 + z) (-3(-7 + z) + z(-7 + z)) = 0 ((-7 * -3 + z * -3) + z(-7 + z)) = 0 ((21 + -3z) + z(-7 + z)) = 0 (21 + -3z + (-7 * z + z * z)) = 0 (21 + -3z + (-7z + z2)) = 0 Combine like terms: -3z + -7z = -10z (21 + -10z + z2) = 0 Solving 21 + -10z + z2 = 0 Solving for variable 'z'. Factor a trinomial. (3 + -1z)(7 + -1z) = 0Subproblem 1
Set the factor '(3 + -1z)' equal to zero and attempt to solve: Simplifying 3 + -1z = 0 Solving 3 + -1z = 0 Move all terms containing z to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + -1z = 0 + -3 Combine like terms: 3 + -3 = 0 0 + -1z = 0 + -3 -1z = 0 + -3 Combine like terms: 0 + -3 = -3 -1z = -3 Divide each side by '-1'. z = 3 Simplifying z = 3Subproblem 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 = {3, 7}
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