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Simplifying -4z(z + -1)(z + 7) = 0 Reorder the terms: -4z(-1 + z)(z + 7) = 0 Reorder the terms: -4z(-1 + z)(7 + z) = 0 Multiply (-1 + z) * (7 + z) -4z(-1(7 + z) + z(7 + z)) = 0 -4z((7 * -1 + z * -1) + z(7 + z)) = 0 -4z((-7 + -1z) + z(7 + z)) = 0 -4z(-7 + -1z + (7 * z + z * z)) = 0 -4z(-7 + -1z + (7z + z2)) = 0 Combine like terms: -1z + 7z = 6z -4z(-7 + 6z + z2) = 0 (-7 * -4z + 6z * -4z + z2 * -4z) = 0 (28z + -24z2 + -4z3) = 0 Solving 28z + -24z2 + -4z3 = 0 Solving for variable 'z'. Factor out the Greatest Common Factor (GCF), '4z'. 4z(7 + -6z + -1z2) = 0 Factor a trinomial. 4z((1 + -1z)(7 + z)) = 0 Ignore the factor 4.Subproblem 1
Set the factor 'z' equal to zero and attempt to solve: Simplifying z = 0 Solving z = 0 Move all terms containing z to the left, all other terms to the right. Simplifying z = 0Subproblem 2
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 3
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 = -7Solution
z = {0, 1, -7}
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