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Simplifying (7z + 9)(7z + 4) = 0 Reorder the terms: (9 + 7z)(7z + 4) = 0 Reorder the terms: (9 + 7z)(4 + 7z) = 0 Multiply (9 + 7z) * (4 + 7z) (9(4 + 7z) + 7z * (4 + 7z)) = 0 ((4 * 9 + 7z * 9) + 7z * (4 + 7z)) = 0 ((36 + 63z) + 7z * (4 + 7z)) = 0 (36 + 63z + (4 * 7z + 7z * 7z)) = 0 (36 + 63z + (28z + 49z2)) = 0 Combine like terms: 63z + 28z = 91z (36 + 91z + 49z2) = 0 Solving 36 + 91z + 49z2 = 0 Solving for variable 'z'. Factor a trinomial. (9 + 7z)(4 + 7z) = 0Subproblem 1
Set the factor '(9 + 7z)' equal to zero and attempt to solve: Simplifying 9 + 7z = 0 Solving 9 + 7z = 0 Move all terms containing z to the left, all other terms to the right. Add '-9' to each side of the equation. 9 + -9 + 7z = 0 + -9 Combine like terms: 9 + -9 = 0 0 + 7z = 0 + -9 7z = 0 + -9 Combine like terms: 0 + -9 = -9 7z = -9 Divide each side by '7'. z = -1.285714286 Simplifying z = -1.285714286Subproblem 2
Set the factor '(4 + 7z)' equal to zero and attempt to solve: Simplifying 4 + 7z = 0 Solving 4 + 7z = 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 + 7z = 0 + -4 Combine like terms: 4 + -4 = 0 0 + 7z = 0 + -4 7z = 0 + -4 Combine like terms: 0 + -4 = -4 7z = -4 Divide each side by '7'. z = -0.5714285714 Simplifying z = -0.5714285714Solution
z = {-1.285714286, -0.5714285714}
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