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Simplifying (5z + -3)(z + 7) + -1(5z + -3)(z + -6) = 0 Reorder the terms: (-3 + 5z)(z + 7) + -1(5z + -3)(z + -6) = 0 Reorder the terms: (-3 + 5z)(7 + z) + -1(5z + -3)(z + -6) = 0 Multiply (-3 + 5z) * (7 + z) (-3(7 + z) + 5z * (7 + z)) + -1(5z + -3)(z + -6) = 0 ((7 * -3 + z * -3) + 5z * (7 + z)) + -1(5z + -3)(z + -6) = 0 ((-21 + -3z) + 5z * (7 + z)) + -1(5z + -3)(z + -6) = 0 (-21 + -3z + (7 * 5z + z * 5z)) + -1(5z + -3)(z + -6) = 0 (-21 + -3z + (35z + 5z2)) + -1(5z + -3)(z + -6) = 0 Combine like terms: -3z + 35z = 32z (-21 + 32z + 5z2) + -1(5z + -3)(z + -6) = 0 Reorder the terms: -21 + 32z + 5z2 + -1(-3 + 5z)(z + -6) = 0 Reorder the terms: -21 + 32z + 5z2 + -1(-3 + 5z)(-6 + z) = 0 Multiply (-3 + 5z) * (-6 + z) -21 + 32z + 5z2 + -1(-3(-6 + z) + 5z * (-6 + z)) = 0 -21 + 32z + 5z2 + -1((-6 * -3 + z * -3) + 5z * (-6 + z)) = 0 -21 + 32z + 5z2 + -1((18 + -3z) + 5z * (-6 + z)) = 0 -21 + 32z + 5z2 + -1(18 + -3z + (-6 * 5z + z * 5z)) = 0 -21 + 32z + 5z2 + -1(18 + -3z + (-30z + 5z2)) = 0 Combine like terms: -3z + -30z = -33z -21 + 32z + 5z2 + -1(18 + -33z + 5z2) = 0 -21 + 32z + 5z2 + (18 * -1 + -33z * -1 + 5z2 * -1) = 0 -21 + 32z + 5z2 + (-18 + 33z + -5z2) = 0 Reorder the terms: -21 + -18 + 32z + 33z + 5z2 + -5z2 = 0 Combine like terms: -21 + -18 = -39 -39 + 32z + 33z + 5z2 + -5z2 = 0 Combine like terms: 32z + 33z = 65z -39 + 65z + 5z2 + -5z2 = 0 Combine like terms: 5z2 + -5z2 = 0 -39 + 65z + 0 = 0 -39 + 65z = 0 Solving -39 + 65z = 0 Solving for variable 'z'. Move all terms containing z to the left, all other terms to the right. Add '39' to each side of the equation. -39 + 39 + 65z = 0 + 39 Combine like terms: -39 + 39 = 0 0 + 65z = 0 + 39 65z = 0 + 39 Combine like terms: 0 + 39 = 39 65z = 39 Divide each side by '65'. z = 0.6 Simplifying z = 0.6
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