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Simplifying (7z + -3)(z + 7) + -1(7z + -3)(z + -6) = 0 Reorder the terms: (-3 + 7z)(z + 7) + -1(7z + -3)(z + -6) = 0 Reorder the terms: (-3 + 7z)(7 + z) + -1(7z + -3)(z + -6) = 0 Multiply (-3 + 7z) * (7 + z) (-3(7 + z) + 7z * (7 + z)) + -1(7z + -3)(z + -6) = 0 ((7 * -3 + z * -3) + 7z * (7 + z)) + -1(7z + -3)(z + -6) = 0 ((-21 + -3z) + 7z * (7 + z)) + -1(7z + -3)(z + -6) = 0 (-21 + -3z + (7 * 7z + z * 7z)) + -1(7z + -3)(z + -6) = 0 (-21 + -3z + (49z + 7z2)) + -1(7z + -3)(z + -6) = 0 Combine like terms: -3z + 49z = 46z (-21 + 46z + 7z2) + -1(7z + -3)(z + -6) = 0 Reorder the terms: -21 + 46z + 7z2 + -1(-3 + 7z)(z + -6) = 0 Reorder the terms: -21 + 46z + 7z2 + -1(-3 + 7z)(-6 + z) = 0 Multiply (-3 + 7z) * (-6 + z) -21 + 46z + 7z2 + -1(-3(-6 + z) + 7z * (-6 + z)) = 0 -21 + 46z + 7z2 + -1((-6 * -3 + z * -3) + 7z * (-6 + z)) = 0 -21 + 46z + 7z2 + -1((18 + -3z) + 7z * (-6 + z)) = 0 -21 + 46z + 7z2 + -1(18 + -3z + (-6 * 7z + z * 7z)) = 0 -21 + 46z + 7z2 + -1(18 + -3z + (-42z + 7z2)) = 0 Combine like terms: -3z + -42z = -45z -21 + 46z + 7z2 + -1(18 + -45z + 7z2) = 0 -21 + 46z + 7z2 + (18 * -1 + -45z * -1 + 7z2 * -1) = 0 -21 + 46z + 7z2 + (-18 + 45z + -7z2) = 0 Reorder the terms: -21 + -18 + 46z + 45z + 7z2 + -7z2 = 0 Combine like terms: -21 + -18 = -39 -39 + 46z + 45z + 7z2 + -7z2 = 0 Combine like terms: 46z + 45z = 91z -39 + 91z + 7z2 + -7z2 = 0 Combine like terms: 7z2 + -7z2 = 0 -39 + 91z + 0 = 0 -39 + 91z = 0 Solving -39 + 91z = 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 + 91z = 0 + 39 Combine like terms: -39 + 39 = 0 0 + 91z = 0 + 39 91z = 0 + 39 Combine like terms: 0 + 39 = 39 91z = 39 Divide each side by '91'. z = 0.4285714286 Simplifying z = 0.4285714286
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