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Simplifying (7 + -1z)(5z + -4) = 0 Reorder the terms: (7 + -1z)(-4 + 5z) = 0 Multiply (7 + -1z) * (-4 + 5z) (7(-4 + 5z) + -1z * (-4 + 5z)) = 0 ((-4 * 7 + 5z * 7) + -1z * (-4 + 5z)) = 0 ((-28 + 35z) + -1z * (-4 + 5z)) = 0 (-28 + 35z + (-4 * -1z + 5z * -1z)) = 0 (-28 + 35z + (4z + -5z2)) = 0 Combine like terms: 35z + 4z = 39z (-28 + 39z + -5z2) = 0 Solving -28 + 39z + -5z2 = 0 Solving for variable 'z'. Factor a trinomial. (-7 + z)(4 + -5z) = 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 '(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 = {7, 0.8}
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