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Simplifying (4 + 3z)(5 + 4z) = 0 Multiply (4 + 3z) * (5 + 4z) (4(5 + 4z) + 3z * (5 + 4z)) = 0 ((5 * 4 + 4z * 4) + 3z * (5 + 4z)) = 0 ((20 + 16z) + 3z * (5 + 4z)) = 0 (20 + 16z + (5 * 3z + 4z * 3z)) = 0 (20 + 16z + (15z + 12z2)) = 0 Combine like terms: 16z + 15z = 31z (20 + 31z + 12z2) = 0 Solving 20 + 31z + 12z2 = 0 Solving for variable 'z'. Factor a trinomial. (4 + 3z)(5 + 4z) = 0Subproblem 1
Set the factor '(4 + 3z)' equal to zero and attempt to solve: Simplifying 4 + 3z = 0 Solving 4 + 3z = 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 + 3z = 0 + -4 Combine like terms: 4 + -4 = 0 0 + 3z = 0 + -4 3z = 0 + -4 Combine like terms: 0 + -4 = -4 3z = -4 Divide each side by '3'. z = -1.333333333 Simplifying z = -1.333333333Subproblem 2
Set the factor '(5 + 4z)' equal to zero and attempt to solve: Simplifying 5 + 4z = 0 Solving 5 + 4z = 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 + 4z = 0 + -5 Combine like terms: 5 + -5 = 0 0 + 4z = 0 + -5 4z = 0 + -5 Combine like terms: 0 + -5 = -5 4z = -5 Divide each side by '4'. z = -1.25 Simplifying z = -1.25Solution
z = {-1.333333333, -1.25}
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