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Simplifying (2 + -1z)(3z + 7) = 0 Reorder the terms: (2 + -1z)(7 + 3z) = 0 Multiply (2 + -1z) * (7 + 3z) (2(7 + 3z) + -1z * (7 + 3z)) = 0 ((7 * 2 + 3z * 2) + -1z * (7 + 3z)) = 0 ((14 + 6z) + -1z * (7 + 3z)) = 0 (14 + 6z + (7 * -1z + 3z * -1z)) = 0 (14 + 6z + (-7z + -3z2)) = 0 Combine like terms: 6z + -7z = -1z (14 + -1z + -3z2) = 0 Solving 14 + -1z + -3z2 = 0 Solving for variable 'z'. Factor a trinomial. (2 + -1z)(7 + 3z) = 0Subproblem 1
Set the factor '(2 + -1z)' equal to zero and attempt to solve: Simplifying 2 + -1z = 0 Solving 2 + -1z = 0 Move all terms containing z to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + -1z = 0 + -2 Combine like terms: 2 + -2 = 0 0 + -1z = 0 + -2 -1z = 0 + -2 Combine like terms: 0 + -2 = -2 -1z = -2 Divide each side by '-1'. z = 2 Simplifying z = 2Subproblem 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 = {2, -2.333333333}
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