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Simplifying (-14z + 1)(5z + 4) + -1(-35z + 3)(2z + -1) = 5 + 2z Reorder the terms: (1 + -14z)(5z + 4) + -1(-35z + 3)(2z + -1) = 5 + 2z Reorder the terms: (1 + -14z)(4 + 5z) + -1(-35z + 3)(2z + -1) = 5 + 2z Multiply (1 + -14z) * (4 + 5z) (1(4 + 5z) + -14z * (4 + 5z)) + -1(-35z + 3)(2z + -1) = 5 + 2z ((4 * 1 + 5z * 1) + -14z * (4 + 5z)) + -1(-35z + 3)(2z + -1) = 5 + 2z ((4 + 5z) + -14z * (4 + 5z)) + -1(-35z + 3)(2z + -1) = 5 + 2z (4 + 5z + (4 * -14z + 5z * -14z)) + -1(-35z + 3)(2z + -1) = 5 + 2z (4 + 5z + (-56z + -70z2)) + -1(-35z + 3)(2z + -1) = 5 + 2z Combine like terms: 5z + -56z = -51z (4 + -51z + -70z2) + -1(-35z + 3)(2z + -1) = 5 + 2z Reorder the terms: 4 + -51z + -70z2 + -1(3 + -35z)(2z + -1) = 5 + 2z Reorder the terms: 4 + -51z + -70z2 + -1(3 + -35z)(-1 + 2z) = 5 + 2z Multiply (3 + -35z) * (-1 + 2z) 4 + -51z + -70z2 + -1(3(-1 + 2z) + -35z * (-1 + 2z)) = 5 + 2z 4 + -51z + -70z2 + -1((-1 * 3 + 2z * 3) + -35z * (-1 + 2z)) = 5 + 2z 4 + -51z + -70z2 + -1((-3 + 6z) + -35z * (-1 + 2z)) = 5 + 2z 4 + -51z + -70z2 + -1(-3 + 6z + (-1 * -35z + 2z * -35z)) = 5 + 2z 4 + -51z + -70z2 + -1(-3 + 6z + (35z + -70z2)) = 5 + 2z Combine like terms: 6z + 35z = 41z 4 + -51z + -70z2 + -1(-3 + 41z + -70z2) = 5 + 2z 4 + -51z + -70z2 + (-3 * -1 + 41z * -1 + -70z2 * -1) = 5 + 2z 4 + -51z + -70z2 + (3 + -41z + 70z2) = 5 + 2z Reorder the terms: 4 + 3 + -51z + -41z + -70z2 + 70z2 = 5 + 2z Combine like terms: 4 + 3 = 7 7 + -51z + -41z + -70z2 + 70z2 = 5 + 2z Combine like terms: -51z + -41z = -92z 7 + -92z + -70z2 + 70z2 = 5 + 2z Combine like terms: -70z2 + 70z2 = 0 7 + -92z + 0 = 5 + 2z 7 + -92z = 5 + 2z Solving 7 + -92z = 5 + 2z Solving for variable 'z'. Move all terms containing z to the left, all other terms to the right. Add '-2z' to each side of the equation. 7 + -92z + -2z = 5 + 2z + -2z Combine like terms: -92z + -2z = -94z 7 + -94z = 5 + 2z + -2z Combine like terms: 2z + -2z = 0 7 + -94z = 5 + 0 7 + -94z = 5 Add '-7' to each side of the equation. 7 + -7 + -94z = 5 + -7 Combine like terms: 7 + -7 = 0 0 + -94z = 5 + -7 -94z = 5 + -7 Combine like terms: 5 + -7 = -2 -94z = -2 Divide each side by '-94'. z = 0.02127659574 Simplifying z = 0.02127659574
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