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Simplifying (4 + -1z)(2z + -7) = 0 Reorder the terms: (4 + -1z)(-7 + 2z) = 0 Multiply (4 + -1z) * (-7 + 2z) (4(-7 + 2z) + -1z * (-7 + 2z)) = 0 ((-7 * 4 + 2z * 4) + -1z * (-7 + 2z)) = 0 ((-28 + 8z) + -1z * (-7 + 2z)) = 0 (-28 + 8z + (-7 * -1z + 2z * -1z)) = 0 (-28 + 8z + (7z + -2z2)) = 0 Combine like terms: 8z + 7z = 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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