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Simplifying 4(z + 9)(-1z + 3) = 0 Reorder the terms: 4(9 + z)(-1z + 3) = 0 Reorder the terms: 4(9 + z)(3 + -1z) = 0 Multiply (9 + z) * (3 + -1z) 4(9(3 + -1z) + z(3 + -1z)) = 0 4((3 * 9 + -1z * 9) + z(3 + -1z)) = 0 4((27 + -9z) + z(3 + -1z)) = 0 4(27 + -9z + (3 * z + -1z * z)) = 0 4(27 + -9z + (3z + -1z2)) = 0 Combine like terms: -9z + 3z = -6z 4(27 + -6z + -1z2) = 0 (27 * 4 + -6z * 4 + -1z2 * 4) = 0 (108 + -24z + -4z2) = 0 Solving 108 + -24z + -4z2 = 0 Solving for variable 'z'. Factor out the Greatest Common Factor (GCF), '4'. 4(27 + -6z + -1z2) = 0 Factor a trinomial. 4((3 + -1z)(9 + z)) = 0 Ignore the factor 4.Subproblem 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 '(9 + z)' equal to zero and attempt to solve: Simplifying 9 + z = 0 Solving 9 + z = 0 Move all terms containing z to the left, all other terms to the right. Add '-9' to each side of the equation. 9 + -9 + z = 0 + -9 Combine like terms: 9 + -9 = 0 0 + z = 0 + -9 z = 0 + -9 Combine like terms: 0 + -9 = -9 z = -9 Simplifying z = -9Solution
z = {3, -9}
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