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Simplifying (7z + 3)(z + 5) = 0 Reorder the terms: (3 + 7z)(z + 5) = 0 Reorder the terms: (3 + 7z)(5 + z) = 0 Multiply (3 + 7z) * (5 + z) (3(5 + z) + 7z * (5 + z)) = 0 ((5 * 3 + z * 3) + 7z * (5 + z)) = 0 ((15 + 3z) + 7z * (5 + z)) = 0 (15 + 3z + (5 * 7z + z * 7z)) = 0 (15 + 3z + (35z + 7z2)) = 0 Combine like terms: 3z + 35z = 38z (15 + 38z + 7z2) = 0 Solving 15 + 38z + 7z2 = 0 Solving for variable 'z'. Factor a trinomial. (5 + z)(3 + 7z) = 0Subproblem 1
Set the factor '(5 + z)' equal to zero and attempt to solve: Simplifying 5 + z = 0 Solving 5 + z = 0 Move all terms containing z to the left, all other terms to the right. Add '-5' to each side of the equation. 5 + -5 + z = 0 + -5 Combine like terms: 5 + -5 = 0 0 + z = 0 + -5 z = 0 + -5 Combine like terms: 0 + -5 = -5 z = -5 Simplifying z = -5Subproblem 2
Set the factor '(3 + 7z)' equal to zero and attempt to solve: Simplifying 3 + 7z = 0 Solving 3 + 7z = 0 Move all terms containing z to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + 7z = 0 + -3 Combine like terms: 3 + -3 = 0 0 + 7z = 0 + -3 7z = 0 + -3 Combine like terms: 0 + -3 = -3 7z = -3 Divide each side by '7'. z = -0.4285714286 Simplifying z = -0.4285714286Solution
z = {-5, -0.4285714286}
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