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Simplifying (4z + 1)(7 + z) = 0 Reorder the terms: (1 + 4z)(7 + z) = 0 Multiply (1 + 4z) * (7 + z) (1(7 + z) + 4z * (7 + z)) = 0 ((7 * 1 + z * 1) + 4z * (7 + z)) = 0 ((7 + 1z) + 4z * (7 + z)) = 0 (7 + 1z + (7 * 4z + z * 4z)) = 0 (7 + 1z + (28z + 4z2)) = 0 Combine like terms: 1z + 28z = 29z (7 + 29z + 4z2) = 0 Solving 7 + 29z + 4z2 = 0 Solving for variable 'z'. Factor a trinomial. (7 + z)(1 + 4z) = 0Subproblem 1
Set the factor '(7 + z)' equal to zero and attempt to solve: Simplifying 7 + z = 0 Solving 7 + z = 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 + z = 0 + -7 Combine like terms: 7 + -7 = 0 0 + z = 0 + -7 z = 0 + -7 Combine like terms: 0 + -7 = -7 z = -7 Simplifying z = -7Subproblem 2
Set the factor '(1 + 4z)' equal to zero and attempt to solve: Simplifying 1 + 4z = 0 Solving 1 + 4z = 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 + 4z = 0 + -1 Combine like terms: 1 + -1 = 0 0 + 4z = 0 + -1 4z = 0 + -1 Combine like terms: 0 + -1 = -1 4z = -1 Divide each side by '4'. z = -0.25 Simplifying z = -0.25Solution
z = {-7, -0.25}
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