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Simplifying -3z(z + 7)(z + -1) = 0 Reorder the terms: -3z(7 + z)(z + -1) = 0 Reorder the terms: -3z(7 + z)(-1 + z) = 0 Multiply (7 + z) * (-1 + z) -3z(7(-1 + z) + z(-1 + z)) = 0 -3z((-1 * 7 + z * 7) + z(-1 + z)) = 0 -3z((-7 + 7z) + z(-1 + z)) = 0 -3z(-7 + 7z + (-1 * z + z * z)) = 0 -3z(-7 + 7z + (-1z + z2)) = 0 Combine like terms: 7z + -1z = 6z -3z(-7 + 6z + z2) = 0 (-7 * -3z + 6z * -3z + z2 * -3z) = 0 (21z + -18z2 + -3z3) = 0 Solving 21z + -18z2 + -3z3 = 0 Solving for variable 'z'. Factor out the Greatest Common Factor (GCF), '3z'. 3z(7 + -6z + -1z2) = 0 Factor a trinomial. 3z((1 + -1z)(7 + z)) = 0 Ignore the factor 3.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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