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Simplifying (5z + 7)(8 + z) = 0 Reorder the terms: (7 + 5z)(8 + z) = 0 Multiply (7 + 5z) * (8 + z) (7(8 + z) + 5z * (8 + z)) = 0 ((8 * 7 + z * 7) + 5z * (8 + z)) = 0 ((56 + 7z) + 5z * (8 + z)) = 0 (56 + 7z + (8 * 5z + z * 5z)) = 0 (56 + 7z + (40z + 5z2)) = 0 Combine like terms: 7z + 40z = 47z (56 + 47z + 5z2) = 0 Solving 56 + 47z + 5z2 = 0 Solving for variable 'z'. Factor a trinomial. (8 + z)(7 + 5z) = 0Subproblem 1
Set the factor '(8 + z)' equal to zero and attempt to solve: Simplifying 8 + z = 0 Solving 8 + z = 0 Move all terms containing z to the left, all other terms to the right. Add '-8' to each side of the equation. 8 + -8 + z = 0 + -8 Combine like terms: 8 + -8 = 0 0 + z = 0 + -8 z = 0 + -8 Combine like terms: 0 + -8 = -8 z = -8 Simplifying z = -8Subproblem 2
Set the factor '(7 + 5z)' equal to zero and attempt to solve: Simplifying 7 + 5z = 0 Solving 7 + 5z = 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 + 5z = 0 + -7 Combine like terms: 7 + -7 = 0 0 + 5z = 0 + -7 5z = 0 + -7 Combine like terms: 0 + -7 = -7 5z = -7 Divide each side by '5'. z = -1.4 Simplifying z = -1.4Solution
z = {-8, -1.4}
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