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Simplifying (5 + -1z)(3z + 4) = 0 Reorder the terms: (5 + -1z)(4 + 3z) = 0 Multiply (5 + -1z) * (4 + 3z) (5(4 + 3z) + -1z * (4 + 3z)) = 0 ((4 * 5 + 3z * 5) + -1z * (4 + 3z)) = 0 ((20 + 15z) + -1z * (4 + 3z)) = 0 (20 + 15z + (4 * -1z + 3z * -1z)) = 0 (20 + 15z + (-4z + -3z2)) = 0 Combine like terms: 15z + -4z = 11z (20 + 11z + -3z2) = 0 Solving 20 + 11z + -3z2 = 0 Solving for variable 'z'. Factor a trinomial. (5 + -1z)(4 + 3z) = 0Subproblem 1
Set the factor '(5 + -1z)' equal to zero and attempt to solve: Simplifying 5 + -1z = 0 Solving 5 + -1z = 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 + -1z = 0 + -5 Combine like terms: 5 + -5 = 0 0 + -1z = 0 + -5 -1z = 0 + -5 Combine like terms: 0 + -5 = -5 -1z = -5 Divide each side by '-1'. z = 5 Simplifying z = 5Subproblem 2
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 = -1.333333333Solution
z = {5, -1.333333333}
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