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Simplifying (5z + -8)(2 + z) = 0 Reorder the terms: (-8 + 5z)(2 + z) = 0 Multiply (-8 + 5z) * (2 + z) (-8(2 + z) + 5z * (2 + z)) = 0 ((2 * -8 + z * -8) + 5z * (2 + z)) = 0 ((-16 + -8z) + 5z * (2 + z)) = 0 (-16 + -8z + (2 * 5z + z * 5z)) = 0 (-16 + -8z + (10z + 5z2)) = 0 Combine like terms: -8z + 10z = 2z (-16 + 2z + 5z2) = 0 Solving -16 + 2z + 5z2 = 0 Solving for variable 'z'. Factor a trinomial. (-2 + -1z)(8 + -5z) = 0Subproblem 1
Set the factor '(-2 + -1z)' equal to zero and attempt to solve: Simplifying -2 + -1z = 0 Solving -2 + -1z = 0 Move all terms containing z to the left, all other terms to the right. Add '2' to each side of the equation. -2 + 2 + -1z = 0 + 2 Combine like terms: -2 + 2 = 0 0 + -1z = 0 + 2 -1z = 0 + 2 Combine like terms: 0 + 2 = 2 -1z = 2 Divide each side by '-1'. z = -2 Simplifying z = -2Subproblem 2
Set the factor '(8 + -5z)' equal to zero and attempt to solve: Simplifying 8 + -5z = 0 Solving 8 + -5z = 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 + -5z = 0 + -8 Combine like terms: 8 + -8 = 0 0 + -5z = 0 + -8 -5z = 0 + -8 Combine like terms: 0 + -8 = -8 -5z = -8 Divide each side by '-5'. z = 1.6 Simplifying z = 1.6Solution
z = {-2, 1.6}
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