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Simplifying (5z + -3)(z + 6) + -1(5z + -3)(z + -5) = 0 Reorder the terms: (-3 + 5z)(z + 6) + -1(5z + -3)(z + -5) = 0 Reorder the terms: (-3 + 5z)(6 + z) + -1(5z + -3)(z + -5) = 0 Multiply (-3 + 5z) * (6 + z) (-3(6 + z) + 5z * (6 + z)) + -1(5z + -3)(z + -5) = 0 ((6 * -3 + z * -3) + 5z * (6 + z)) + -1(5z + -3)(z + -5) = 0 ((-18 + -3z) + 5z * (6 + z)) + -1(5z + -3)(z + -5) = 0 (-18 + -3z + (6 * 5z + z * 5z)) + -1(5z + -3)(z + -5) = 0 (-18 + -3z + (30z + 5z2)) + -1(5z + -3)(z + -5) = 0 Combine like terms: -3z + 30z = 27z (-18 + 27z + 5z2) + -1(5z + -3)(z + -5) = 0 Reorder the terms: -18 + 27z + 5z2 + -1(-3 + 5z)(z + -5) = 0 Reorder the terms: -18 + 27z + 5z2 + -1(-3 + 5z)(-5 + z) = 0 Multiply (-3 + 5z) * (-5 + z) -18 + 27z + 5z2 + -1(-3(-5 + z) + 5z * (-5 + z)) = 0 -18 + 27z + 5z2 + -1((-5 * -3 + z * -3) + 5z * (-5 + z)) = 0 -18 + 27z + 5z2 + -1((15 + -3z) + 5z * (-5 + z)) = 0 -18 + 27z + 5z2 + -1(15 + -3z + (-5 * 5z + z * 5z)) = 0 -18 + 27z + 5z2 + -1(15 + -3z + (-25z + 5z2)) = 0 Combine like terms: -3z + -25z = -28z -18 + 27z + 5z2 + -1(15 + -28z + 5z2) = 0 -18 + 27z + 5z2 + (15 * -1 + -28z * -1 + 5z2 * -1) = 0 -18 + 27z + 5z2 + (-15 + 28z + -5z2) = 0 Reorder the terms: -18 + -15 + 27z + 28z + 5z2 + -5z2 = 0 Combine like terms: -18 + -15 = -33 -33 + 27z + 28z + 5z2 + -5z2 = 0 Combine like terms: 27z + 28z = 55z -33 + 55z + 5z2 + -5z2 = 0 Combine like terms: 5z2 + -5z2 = 0 -33 + 55z + 0 = 0 -33 + 55z = 0 Solving -33 + 55z = 0 Solving for variable 'z'. Move all terms containing z to the left, all other terms to the right. Add '33' to each side of the equation. -33 + 33 + 55z = 0 + 33 Combine like terms: -33 + 33 = 0 0 + 55z = 0 + 33 55z = 0 + 33 Combine like terms: 0 + 33 = 33 55z = 33 Divide each side by '55'. z = 0.6 Simplifying z = 0.6
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