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Simplifying (2z + -3)(5 + z) = 0 Reorder the terms: (-3 + 2z)(5 + z) = 0 Multiply (-3 + 2z) * (5 + z) (-3(5 + z) + 2z * (5 + z)) = 0 ((5 * -3 + z * -3) + 2z * (5 + z)) = 0 ((-15 + -3z) + 2z * (5 + z)) = 0 (-15 + -3z + (5 * 2z + z * 2z)) = 0 (-15 + -3z + (10z + 2z2)) = 0 Combine like terms: -3z + 10z = 7z (-15 + 7z + 2z2) = 0 Solving -15 + 7z + 2z2 = 0 Solving for variable 'z'. Factor a trinomial. (-5 + -1z)(3 + -2z) = 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 '(3 + -2z)' equal to zero and attempt to solve: Simplifying 3 + -2z = 0 Solving 3 + -2z = 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 + -2z = 0 + -3 Combine like terms: 3 + -3 = 0 0 + -2z = 0 + -3 -2z = 0 + -3 Combine like terms: 0 + -3 = -3 -2z = -3 Divide each side by '-2'. z = 1.5 Simplifying z = 1.5Solution
z = {-5, 1.5}
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