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Simplifying (4z + 4)(17z + -1) = 4 + (34z + 4)(2z + -1) + 6z Reorder the terms: (4 + 4z)(17z + -1) = 4 + (34z + 4)(2z + -1) + 6z Reorder the terms: (4 + 4z)(-1 + 17z) = 4 + (34z + 4)(2z + -1) + 6z Multiply (4 + 4z) * (-1 + 17z) (4(-1 + 17z) + 4z * (-1 + 17z)) = 4 + (34z + 4)(2z + -1) + 6z ((-1 * 4 + 17z * 4) + 4z * (-1 + 17z)) = 4 + (34z + 4)(2z + -1) + 6z ((-4 + 68z) + 4z * (-1 + 17z)) = 4 + (34z + 4)(2z + -1) + 6z (-4 + 68z + (-1 * 4z + 17z * 4z)) = 4 + (34z + 4)(2z + -1) + 6z (-4 + 68z + (-4z + 68z2)) = 4 + (34z + 4)(2z + -1) + 6z Combine like terms: 68z + -4z = 64z (-4 + 64z + 68z2) = 4 + (34z + 4)(2z + -1) + 6z Reorder the terms: -4 + 64z + 68z2 = 4 + (4 + 34z)(2z + -1) + 6z Reorder the terms: -4 + 64z + 68z2 = 4 + (4 + 34z)(-1 + 2z) + 6z Multiply (4 + 34z) * (-1 + 2z) -4 + 64z + 68z2 = 4 + (4(-1 + 2z) + 34z * (-1 + 2z)) + 6z -4 + 64z + 68z2 = 4 + ((-1 * 4 + 2z * 4) + 34z * (-1 + 2z)) + 6z -4 + 64z + 68z2 = 4 + ((-4 + 8z) + 34z * (-1 + 2z)) + 6z -4 + 64z + 68z2 = 4 + (-4 + 8z + (-1 * 34z + 2z * 34z)) + 6z -4 + 64z + 68z2 = 4 + (-4 + 8z + (-34z + 68z2)) + 6z Combine like terms: 8z + -34z = -26z -4 + 64z + 68z2 = 4 + (-4 + -26z + 68z2) + 6z Reorder the terms: -4 + 64z + 68z2 = 4 + -4 + -26z + 6z + 68z2 Combine like terms: 4 + -4 = 0 -4 + 64z + 68z2 = 0 + -26z + 6z + 68z2 -4 + 64z + 68z2 = -26z + 6z + 68z2 Combine like terms: -26z + 6z = -20z -4 + 64z + 68z2 = -20z + 68z2 Add '-68z2' to each side of the equation. -4 + 64z + 68z2 + -68z2 = -20z + 68z2 + -68z2 Combine like terms: 68z2 + -68z2 = 0 -4 + 64z + 0 = -20z + 68z2 + -68z2 -4 + 64z = -20z + 68z2 + -68z2 Combine like terms: 68z2 + -68z2 = 0 -4 + 64z = -20z + 0 -4 + 64z = -20z Solving -4 + 64z = -20z Solving for variable 'z'. Move all terms containing z to the left, all other terms to the right. Add '20z' to each side of the equation. -4 + 64z + 20z = -20z + 20z Combine like terms: 64z + 20z = 84z -4 + 84z = -20z + 20z Combine like terms: -20z + 20z = 0 -4 + 84z = 0 Add '4' to each side of the equation. -4 + 4 + 84z = 0 + 4 Combine like terms: -4 + 4 = 0 0 + 84z = 0 + 4 84z = 0 + 4 Combine like terms: 0 + 4 = 4 84z = 4 Divide each side by '84'. z = 0.04761904762 Simplifying z = 0.04761904762
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