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Simplifying (4z + 3)(3z + 5) = 0 Reorder the terms: (3 + 4z)(3z + 5) = 0 Reorder the terms: (3 + 4z)(5 + 3z) = 0 Multiply (3 + 4z) * (5 + 3z) (3(5 + 3z) + 4z * (5 + 3z)) = 0 ((5 * 3 + 3z * 3) + 4z * (5 + 3z)) = 0 ((15 + 9z) + 4z * (5 + 3z)) = 0 (15 + 9z + (5 * 4z + 3z * 4z)) = 0 (15 + 9z + (20z + 12z2)) = 0 Combine like terms: 9z + 20z = 29z (15 + 29z + 12z2) = 0 Solving 15 + 29z + 12z2 = 0 Solving for variable 'z'. Factor a trinomial. (5 + 3z)(3 + 4z) = 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 '(3 + 4z)' equal to zero and attempt to solve: Simplifying 3 + 4z = 0 Solving 3 + 4z = 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 + 4z = 0 + -3 Combine like terms: 3 + -3 = 0 0 + 4z = 0 + -3 4z = 0 + -3 Combine like terms: 0 + -3 = -3 4z = -3 Divide each side by '4'. z = -0.75 Simplifying z = -0.75Solution
z = {-1.666666667, -0.75}
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