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Simplifying (4 + z)(2z + 7) = 0 Reorder the terms: (4 + z)(7 + 2z) = 0 Multiply (4 + z) * (7 + 2z) (4(7 + 2z) + z(7 + 2z)) = 0 ((7 * 4 + 2z * 4) + z(7 + 2z)) = 0 ((28 + 8z) + z(7 + 2z)) = 0 (28 + 8z + (7 * z + 2z * z)) = 0 (28 + 8z + (7z + 2z2)) = 0 Combine like terms: 8z + 7z = 15z (28 + 15z + 2z2) = 0 Solving 28 + 15z + 2z2 = 0 Solving for variable 'z'. Factor a trinomial. (4 + z)(7 + 2z) = 0Subproblem 1
Set the factor '(4 + z)' equal to zero and attempt to solve: Simplifying 4 + z = 0 Solving 4 + z = 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 + z = 0 + -4 Combine like terms: 4 + -4 = 0 0 + z = 0 + -4 z = 0 + -4 Combine like terms: 0 + -4 = -4 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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