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Simplifying (3z + 5)(7z + 4) = 0 Reorder the terms: (5 + 3z)(7z + 4) = 0 Reorder the terms: (5 + 3z)(4 + 7z) = 0 Multiply (5 + 3z) * (4 + 7z) (5(4 + 7z) + 3z * (4 + 7z)) = 0 ((4 * 5 + 7z * 5) + 3z * (4 + 7z)) = 0 ((20 + 35z) + 3z * (4 + 7z)) = 0 (20 + 35z + (4 * 3z + 7z * 3z)) = 0 (20 + 35z + (12z + 21z2)) = 0 Combine like terms: 35z + 12z = 47z (20 + 47z + 21z2) = 0 Solving 20 + 47z + 21z2 = 0 Solving for variable 'z'. Factor a trinomial. (5 + 3z)(4 + 7z) = 0Subproblem 1
Set the factor '(5 + 3z)' equal to zero and attempt to solve: Simplifying 5 + 3z = 0 Solving 5 + 3z = 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 + 3z = 0 + -5 Combine like terms: 5 + -5 = 0 0 + 3z = 0 + -5 3z = 0 + -5 Combine like terms: 0 + -5 = -5 3z = -5 Divide each side by '3'. z = -1.666666667 Simplifying z = -1.666666667Subproblem 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 = {-1.666666667, -0.5714285714}
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