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Simplifying -4(z + 2)(-1z + -7) = 0 Reorder the terms: -4(2 + z)(-1z + -7) = 0 Reorder the terms: -4(2 + z)(-7 + -1z) = 0 Multiply (2 + z) * (-7 + -1z) -4(2(-7 + -1z) + z(-7 + -1z)) = 0 -4((-7 * 2 + -1z * 2) + z(-7 + -1z)) = 0 -4((-14 + -2z) + z(-7 + -1z)) = 0 -4(-14 + -2z + (-7 * z + -1z * z)) = 0 -4(-14 + -2z + (-7z + -1z2)) = 0 Combine like terms: -2z + -7z = -9z -4(-14 + -9z + -1z2) = 0 (-14 * -4 + -9z * -4 + -1z2 * -4) = 0 (56 + 36z + 4z2) = 0 Solving 56 + 36z + 4z2 = 0 Solving for variable 'z'. Factor out the Greatest Common Factor (GCF), '4'. 4(14 + 9z + z2) = 0 Factor a trinomial. 4((7 + z)(2 + z)) = 0 Ignore the factor 4.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 '(2 + z)' equal to zero and attempt to solve: Simplifying 2 + z = 0 Solving 2 + z = 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 + z = 0 + -2 Combine like terms: 2 + -2 = 0 0 + z = 0 + -2 z = 0 + -2 Combine like terms: 0 + -2 = -2 z = -2 Simplifying z = -2Solution
z = {-7, -2}
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