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Simplifying (3z + 1)(6 + -1z) = 0 Reorder the terms: (1 + 3z)(6 + -1z) = 0 Multiply (1 + 3z) * (6 + -1z) (1(6 + -1z) + 3z * (6 + -1z)) = 0 ((6 * 1 + -1z * 1) + 3z * (6 + -1z)) = 0 ((6 + -1z) + 3z * (6 + -1z)) = 0 (6 + -1z + (6 * 3z + -1z * 3z)) = 0 (6 + -1z + (18z + -3z2)) = 0 Combine like terms: -1z + 18z = 17z (6 + 17z + -3z2) = 0 Solving 6 + 17z + -3z2 = 0 Solving for variable 'z'. Factor a trinomial. (6 + -1z)(1 + 3z) = 0Subproblem 1
Set the factor '(6 + -1z)' equal to zero and attempt to solve: Simplifying 6 + -1z = 0 Solving 6 + -1z = 0 Move all terms containing z to the left, all other terms to the right. Add '-6' to each side of the equation. 6 + -6 + -1z = 0 + -6 Combine like terms: 6 + -6 = 0 0 + -1z = 0 + -6 -1z = 0 + -6 Combine like terms: 0 + -6 = -6 -1z = -6 Divide each side by '-1'. z = 6 Simplifying z = 6Subproblem 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 = {6, -0.3333333333}
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