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Simplifying 5(z + 1)(-1z + 9) = 0 Reorder the terms: 5(1 + z)(-1z + 9) = 0 Reorder the terms: 5(1 + z)(9 + -1z) = 0 Multiply (1 + z) * (9 + -1z) 5(1(9 + -1z) + z(9 + -1z)) = 0 5((9 * 1 + -1z * 1) + z(9 + -1z)) = 0 5((9 + -1z) + z(9 + -1z)) = 0 5(9 + -1z + (9 * z + -1z * z)) = 0 5(9 + -1z + (9z + -1z2)) = 0 Combine like terms: -1z + 9z = 8z 5(9 + 8z + -1z2) = 0 (9 * 5 + 8z * 5 + -1z2 * 5) = 0 (45 + 40z + -5z2) = 0 Solving 45 + 40z + -5z2 = 0 Solving for variable 'z'. Factor out the Greatest Common Factor (GCF), '5'. 5(9 + 8z + -1z2) = 0 Factor a trinomial. 5((9 + -1z)(1 + z)) = 0 Ignore the factor 5.Subproblem 1
Set the factor '(9 + -1z)' equal to zero and attempt to solve: Simplifying 9 + -1z = 0 Solving 9 + -1z = 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 + -1z = 0 + -9 Combine like terms: 9 + -9 = 0 0 + -1z = 0 + -9 -1z = 0 + -9 Combine like terms: 0 + -9 = -9 -1z = -9 Divide each side by '-1'. z = 9 Simplifying z = 9Subproblem 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 = {9, -1}
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