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Simplifying 3(z + 7)(-1z + -1) = 0 Reorder the terms: 3(7 + z)(-1z + -1) = 0 Reorder the terms: 3(7 + z)(-1 + -1z) = 0 Multiply (7 + z) * (-1 + -1z) 3(7(-1 + -1z) + z(-1 + -1z)) = 0 3((-1 * 7 + -1z * 7) + z(-1 + -1z)) = 0 3((-7 + -7z) + z(-1 + -1z)) = 0 3(-7 + -7z + (-1 * z + -1z * z)) = 0 3(-7 + -7z + (-1z + -1z2)) = 0 Combine like terms: -7z + -1z = -8z 3(-7 + -8z + -1z2) = 0 (-7 * 3 + -8z * 3 + -1z2 * 3) = 0 (-21 + -24z + -3z2) = 0 Solving -21 + -24z + -3z2 = 0 Solving for variable 'z'. Factor out the Greatest Common Factor (GCF), '-3'. -3(7 + 8z + z2) = 0 Factor a trinomial. -3((7 + z)(1 + z)) = 0 Ignore the factor -3.Subproblem 1
Set the factor '(7 + z)' equal to zero and attempt to solve: Simplifying 7 + z = 0 Solving 7 + z = 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 + z = 0 + -7 Combine like terms: 7 + -7 = 0 0 + z = 0 + -7 z = 0 + -7 Combine like terms: 0 + -7 = -7 z = -7 Simplifying z = -7Subproblem 2
Set the factor '(1 + z)' equal to zero and attempt to solve: Simplifying 1 + z = 0 Solving 1 + z = 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 + z = 0 + -1 Combine like terms: 1 + -1 = 0 0 + z = 0 + -1 z = 0 + -1 Combine like terms: 0 + -1 = -1 z = -1 Simplifying z = -1Solution
z = {-7, -1}
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