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Simplifying (5z + -4)(6 + z) = 0 Reorder the terms: (-4 + 5z)(6 + z) = 0 Multiply (-4 + 5z) * (6 + z) (-4(6 + z) + 5z * (6 + z)) = 0 ((6 * -4 + z * -4) + 5z * (6 + z)) = 0 ((-24 + -4z) + 5z * (6 + z)) = 0 (-24 + -4z + (6 * 5z + z * 5z)) = 0 (-24 + -4z + (30z + 5z2)) = 0 Combine like terms: -4z + 30z = 26z (-24 + 26z + 5z2) = 0 Solving -24 + 26z + 5z2 = 0 Solving for variable 'z'. Factor a trinomial. (-6 + -1z)(4 + -5z) = 0Subproblem 1
Set the factor '(-6 + -1z)' equal to zero and attempt to solve: Simplifying -6 + -1z = 0 Solving -6 + -1z = 0 Move all terms containing z to the left, all other terms to the right. Add '6' to each side of the equation. -6 + 6 + -1z = 0 + 6 Combine like terms: -6 + 6 = 0 0 + -1z = 0 + 6 -1z = 0 + 6 Combine like terms: 0 + 6 = 6 -1z = 6 Divide each side by '-1'. z = -6 Simplifying z = -6Subproblem 2
Set the factor '(4 + -5z)' equal to zero and attempt to solve: Simplifying 4 + -5z = 0 Solving 4 + -5z = 0 Move all terms containing z to the left, all other terms to the right. Add '-4' to each side of the equation. 4 + -4 + -5z = 0 + -4 Combine like terms: 4 + -4 = 0 0 + -5z = 0 + -4 -5z = 0 + -4 Combine like terms: 0 + -4 = -4 -5z = -4 Divide each side by '-5'. z = 0.8 Simplifying z = 0.8Solution
z = {-6, 0.8}
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