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Simplifying (3z + 7)(3 + -1z) = 0 Reorder the terms: (7 + 3z)(3 + -1z) = 0 Multiply (7 + 3z) * (3 + -1z) (7(3 + -1z) + 3z * (3 + -1z)) = 0 ((3 * 7 + -1z * 7) + 3z * (3 + -1z)) = 0 ((21 + -7z) + 3z * (3 + -1z)) = 0 (21 + -7z + (3 * 3z + -1z * 3z)) = 0 (21 + -7z + (9z + -3z2)) = 0 Combine like terms: -7z + 9z = 2z (21 + 2z + -3z2) = 0 Solving 21 + 2z + -3z2 = 0 Solving for variable 'z'. Factor a trinomial. (3 + -1z)(7 + 3z) = 0Subproblem 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 '(7 + 3z)' equal to zero and attempt to solve: Simplifying 7 + 3z = 0 Solving 7 + 3z = 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 + 3z = 0 + -7 Combine like terms: 7 + -7 = 0 0 + 3z = 0 + -7 3z = 0 + -7 Combine like terms: 0 + -7 = -7 3z = -7 Divide each side by '3'. z = -2.333333333 Simplifying z = -2.333333333Solution
z = {3, -2.333333333}
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