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Simplifying (5 + -1z)(4z + -7) = 0 Reorder the terms: (5 + -1z)(-7 + 4z) = 0 Multiply (5 + -1z) * (-7 + 4z) (5(-7 + 4z) + -1z * (-7 + 4z)) = 0 ((-7 * 5 + 4z * 5) + -1z * (-7 + 4z)) = 0 ((-35 + 20z) + -1z * (-7 + 4z)) = 0 (-35 + 20z + (-7 * -1z + 4z * -1z)) = 0 (-35 + 20z + (7z + -4z2)) = 0 Combine like terms: 20z + 7z = 27z (-35 + 27z + -4z2) = 0 Solving -35 + 27z + -4z2 = 0 Solving for variable 'z'. Factor a trinomial. (-5 + z)(7 + -4z) = 0Subproblem 1
Set the factor '(-5 + z)' equal to zero and attempt to solve: Simplifying -5 + z = 0 Solving -5 + z = 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 + z = 0 + 5 Combine like terms: -5 + 5 = 0 0 + z = 0 + 5 z = 0 + 5 Combine like terms: 0 + 5 = 5 z = 5 Simplifying z = 5Subproblem 2
Set the factor '(7 + -4z)' equal to zero and attempt to solve: Simplifying 7 + -4z = 0 Solving 7 + -4z = 0 Move all terms containing z to the left, all other terms to the right. Add '-7' to each side of the equation. 7 + -7 + -4z = 0 + -7 Combine like terms: 7 + -7 = 0 0 + -4z = 0 + -7 -4z = 0 + -7 Combine like terms: 0 + -7 = -7 -4z = -7 Divide each side by '-4'. z = 1.75 Simplifying z = 1.75Solution
z = {5, 1.75}
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