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Simplifying (5z + -3)(8 + z) = 0 Reorder the terms: (-3 + 5z)(8 + z) = 0 Multiply (-3 + 5z) * (8 + z) (-3(8 + z) + 5z * (8 + z)) = 0 ((8 * -3 + z * -3) + 5z * (8 + z)) = 0 ((-24 + -3z) + 5z * (8 + z)) = 0 (-24 + -3z + (8 * 5z + z * 5z)) = 0 (-24 + -3z + (40z + 5z2)) = 0 Combine like terms: -3z + 40z = 37z (-24 + 37z + 5z2) = 0 Solving -24 + 37z + 5z2 = 0 Solving for variable 'z'. Factor a trinomial. (-8 + -1z)(3 + -5z) = 0Subproblem 1
Set the factor '(-8 + -1z)' equal to zero and attempt to solve: Simplifying -8 + -1z = 0 Solving -8 + -1z = 0 Move all terms containing z to the left, all other terms to the right. Add '8' to each side of the equation. -8 + 8 + -1z = 0 + 8 Combine like terms: -8 + 8 = 0 0 + -1z = 0 + 8 -1z = 0 + 8 Combine like terms: 0 + 8 = 8 -1z = 8 Divide each side by '-1'. z = -8 Simplifying z = -8Subproblem 2
Set the factor '(3 + -5z)' equal to zero and attempt to solve: Simplifying 3 + -5z = 0 Solving 3 + -5z = 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 + -5z = 0 + -3 Combine like terms: 3 + -3 = 0 0 + -5z = 0 + -3 -5z = 0 + -3 Combine like terms: 0 + -3 = -3 -5z = -3 Divide each side by '-5'. z = 0.6 Simplifying z = 0.6Solution
z = {-8, 0.6}
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