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Simplifying (2z + -7)(4 + -1z) = 0 Reorder the terms: (-7 + 2z)(4 + -1z) = 0 Multiply (-7 + 2z) * (4 + -1z) (-7(4 + -1z) + 2z * (4 + -1z)) = 0 ((4 * -7 + -1z * -7) + 2z * (4 + -1z)) = 0 ((-28 + 7z) + 2z * (4 + -1z)) = 0 (-28 + 7z + (4 * 2z + -1z * 2z)) = 0 (-28 + 7z + (8z + -2z2)) = 0 Combine like terms: 7z + 8z = 15z (-28 + 15z + -2z2) = 0 Solving -28 + 15z + -2z2 = 0 Solving for variable 'z'. Factor a trinomial. (-4 + z)(7 + -2z) = 0Subproblem 1
Set the factor '(-4 + z)' equal to zero and attempt to solve: Simplifying -4 + z = 0 Solving -4 + z = 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 + z = 0 + 4 Combine like terms: -4 + 4 = 0 0 + z = 0 + 4 z = 0 + 4 Combine like terms: 0 + 4 = 4 z = 4 Simplifying z = 4Subproblem 2
Set the factor '(7 + -2z)' equal to zero and attempt to solve: Simplifying 7 + -2z = 0 Solving 7 + -2z = 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 + -2z = 0 + -7 Combine like terms: 7 + -7 = 0 0 + -2z = 0 + -7 -2z = 0 + -7 Combine like terms: 0 + -7 = -7 -2z = -7 Divide each side by '-2'. z = 3.5 Simplifying z = 3.5Solution
z = {4, 3.5}
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