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Simplifying (8 + -1z)(3z + 1) = 0 Reorder the terms: (8 + -1z)(1 + 3z) = 0 Multiply (8 + -1z) * (1 + 3z) (8(1 + 3z) + -1z * (1 + 3z)) = 0 ((1 * 8 + 3z * 8) + -1z * (1 + 3z)) = 0 ((8 + 24z) + -1z * (1 + 3z)) = 0 (8 + 24z + (1 * -1z + 3z * -1z)) = 0 (8 + 24z + (-1z + -3z2)) = 0 Combine like terms: 24z + -1z = 23z (8 + 23z + -3z2) = 0 Solving 8 + 23z + -3z2 = 0 Solving for variable 'z'. Factor a trinomial. (8 + -1z)(1 + 3z) = 0Subproblem 1
Set the factor '(8 + -1z)' equal to zero and attempt to solve: Simplifying 8 + -1z = 0 Solving 8 + -1z = 0 Move all terms containing z to the left, all other terms to the right. Add '-8' to each side of the equation. 8 + -8 + -1z = 0 + -8 Combine like terms: 8 + -8 = 0 0 + -1z = 0 + -8 -1z = 0 + -8 Combine like terms: 0 + -8 = -8 -1z = -8 Divide each side by '-1'. z = 8 Simplifying z = 8Subproblem 2
Set the factor '(1 + 3z)' equal to zero and attempt to solve: Simplifying 1 + 3z = 0 Solving 1 + 3z = 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 + 3z = 0 + -1 Combine like terms: 1 + -1 = 0 0 + 3z = 0 + -1 3z = 0 + -1 Combine like terms: 0 + -1 = -1 3z = -1 Divide each side by '3'. z = -0.3333333333 Simplifying z = -0.3333333333Solution
z = {8, -0.3333333333}
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