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Simplifying (2z + 7)(4 + -1z) = 0 Reorder the terms: (7 + 2z)(4 + -1z) = 0 Multiply (7 + 2z) * (4 + -1z) (7(4 + -1z) + 2z * (4 + -1z)) = 0 ((4 * 7 + -1z * 7) + 2z * (4 + -1z)) = 0 ((28 + -7z) + 2z * (4 + -1z)) = 0 (28 + -7z + (4 * 2z + -1z * 2z)) = 0 (28 + -7z + (8z + -2z2)) = 0 Combine like terms: -7z + 8z = 1z (28 + 1z + -2z2) = 0 Solving 28 + 1z + -2z2 = 0 Solving for variable 'z'. Factor a trinomial. (4 + -1z)(7 + 2z) = 0Subproblem 1
Set the factor '(4 + -1z)' equal to zero and attempt to solve: Simplifying 4 + -1z = 0 Solving 4 + -1z = 0 Move all terms containing z to the left, all other terms to the right. Add '-4' to each side of the equation. 4 + -4 + -1z = 0 + -4 Combine like terms: 4 + -4 = 0 0 + -1z = 0 + -4 -1z = 0 + -4 Combine like terms: 0 + -4 = -4 -1z = -4 Divide each side by '-1'. z = 4 Simplifying z = 4Subproblem 2
Set the factor '(7 + 2z)' equal to zero and attempt to solve: Simplifying 7 + 2z = 0 Solving 7 + 2z = 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 + 2z = 0 + -7 Combine like terms: 7 + -7 = 0 0 + 2z = 0 + -7 2z = 0 + -7 Combine like terms: 0 + -7 = -7 2z = -7 Divide each side by '2'. z = -3.5 Simplifying z = -3.5Solution
z = {4, -3.5}
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