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Simplifying (3z + -1)(5 + z) = 0 Reorder the terms: (-1 + 3z)(5 + z) = 0 Multiply (-1 + 3z) * (5 + z) (-1(5 + z) + 3z * (5 + z)) = 0 ((5 * -1 + z * -1) + 3z * (5 + z)) = 0 ((-5 + -1z) + 3z * (5 + z)) = 0 (-5 + -1z + (5 * 3z + z * 3z)) = 0 (-5 + -1z + (15z + 3z2)) = 0 Combine like terms: -1z + 15z = 14z (-5 + 14z + 3z2) = 0 Solving -5 + 14z + 3z2 = 0 Solving for variable 'z'. Factor a trinomial. (-5 + -1z)(1 + -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 '(1 + -3z)' equal to zero and attempt to solve: Simplifying 1 + -3z = 0 Solving 1 + -3z = 0 Move all terms containing z to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + -3z = 0 + -1 Combine like terms: 1 + -1 = 0 0 + -3z = 0 + -1 -3z = 0 + -1 Combine like terms: 0 + -1 = -1 -3z = -1 Divide each side by '-3'. z = 0.3333333333 Simplifying z = 0.3333333333Solution
z = {-5, 0.3333333333}
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