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Simplifying (5 + z)(3z + -1) = 0 Reorder the terms: (5 + z)(-1 + 3z) = 0 Multiply (5 + z) * (-1 + 3z) (5(-1 + 3z) + z(-1 + 3z)) = 0 ((-1 * 5 + 3z * 5) + z(-1 + 3z)) = 0 ((-5 + 15z) + z(-1 + 3z)) = 0 (-5 + 15z + (-1 * z + 3z * z)) = 0 (-5 + 15z + (-1z + 3z2)) = 0 Combine like terms: 15z + -1z = 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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