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Simplifying (4z + -1)(7 + -1z) = 0 Reorder the terms: (-1 + 4z)(7 + -1z) = 0 Multiply (-1 + 4z) * (7 + -1z) (-1(7 + -1z) + 4z * (7 + -1z)) = 0 ((7 * -1 + -1z * -1) + 4z * (7 + -1z)) = 0 ((-7 + 1z) + 4z * (7 + -1z)) = 0 (-7 + 1z + (7 * 4z + -1z * 4z)) = 0 (-7 + 1z + (28z + -4z2)) = 0 Combine like terms: 1z + 28z = 29z (-7 + 29z + -4z2) = 0 Solving -7 + 29z + -4z2 = 0 Solving for variable 'z'. Factor a trinomial. (-7 + z)(1 + -4z) = 0Subproblem 1
Set the factor '(-7 + z)' equal to zero and attempt to solve: Simplifying -7 + z = 0 Solving -7 + z = 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 + z = 0 + 7 Combine like terms: -7 + 7 = 0 0 + z = 0 + 7 z = 0 + 7 Combine like terms: 0 + 7 = 7 z = 7 Simplifying z = 7Subproblem 2
Set the factor '(1 + -4z)' equal to zero and attempt to solve: Simplifying 1 + -4z = 0 Solving 1 + -4z = 0 Move all terms containing z to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + -4z = 0 + -1 Combine like terms: 1 + -1 = 0 0 + -4z = 0 + -1 -4z = 0 + -1 Combine like terms: 0 + -1 = -1 -4z = -1 Divide each side by '-4'. z = 0.25 Simplifying z = 0.25Solution
z = {7, 0.25}
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