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Simplifying (z + 1)(z + -3) + -1(z + 2)(z + 4) = 3z + -1[4z + -2(z + -1)] Reorder the terms: (1 + z)(z + -3) + -1(z + 2)(z + 4) = 3z + -1[4z + -2(z + -1)] Reorder the terms: (1 + z)(-3 + z) + -1(z + 2)(z + 4) = 3z + -1[4z + -2(z + -1)] Multiply (1 + z) * (-3 + z) (1(-3 + z) + z(-3 + z)) + -1(z + 2)(z + 4) = 3z + -1[4z + -2(z + -1)] ((-3 * 1 + z * 1) + z(-3 + z)) + -1(z + 2)(z + 4) = 3z + -1[4z + -2(z + -1)] ((-3 + 1z) + z(-3 + z)) + -1(z + 2)(z + 4) = 3z + -1[4z + -2(z + -1)] (-3 + 1z + (-3 * z + z * z)) + -1(z + 2)(z + 4) = 3z + -1[4z + -2(z + -1)] (-3 + 1z + (-3z + z2)) + -1(z + 2)(z + 4) = 3z + -1[4z + -2(z + -1)] Combine like terms: 1z + -3z = -2z (-3 + -2z + z2) + -1(z + 2)(z + 4) = 3z + -1[4z + -2(z + -1)] Reorder the terms: -3 + -2z + z2 + -1(2 + z)(z + 4) = 3z + -1[4z + -2(z + -1)] Reorder the terms: -3 + -2z + z2 + -1(2 + z)(4 + z) = 3z + -1[4z + -2(z + -1)] Multiply (2 + z) * (4 + z) -3 + -2z + z2 + -1(2(4 + z) + z(4 + z)) = 3z + -1[4z + -2(z + -1)] -3 + -2z + z2 + -1((4 * 2 + z * 2) + z(4 + z)) = 3z + -1[4z + -2(z + -1)] -3 + -2z + z2 + -1((8 + 2z) + z(4 + z)) = 3z + -1[4z + -2(z + -1)] -3 + -2z + z2 + -1(8 + 2z + (4 * z + z * z)) = 3z + -1[4z + -2(z + -1)] -3 + -2z + z2 + -1(8 + 2z + (4z + z2)) = 3z + -1[4z + -2(z + -1)] Combine like terms: 2z + 4z = 6z -3 + -2z + z2 + -1(8 + 6z + z2) = 3z + -1[4z + -2(z + -1)] -3 + -2z + z2 + (8 * -1 + 6z * -1 + z2 * -1) = 3z + -1[4z + -2(z + -1)] -3 + -2z + z2 + (-8 + -6z + -1z2) = 3z + -1[4z + -2(z + -1)] Reorder the terms: -3 + -8 + -2z + -6z + z2 + -1z2 = 3z + -1[4z + -2(z + -1)] Combine like terms: -3 + -8 = -11 -11 + -2z + -6z + z2 + -1z2 = 3z + -1[4z + -2(z + -1)] Combine like terms: -2z + -6z = -8z -11 + -8z + z2 + -1z2 = 3z + -1[4z + -2(z + -1)] Combine like terms: z2 + -1z2 = 0 -11 + -8z + 0 = 3z + -1[4z + -2(z + -1)] -11 + -8z = 3z + -1[4z + -2(z + -1)] Reorder the terms: -11 + -8z = 3z + -1[4z + -2(-1 + z)] -11 + -8z = 3z + -1[4z + (-1 * -2 + z * -2)] -11 + -8z = 3z + -1[4z + (2 + -2z)] Reorder the terms: -11 + -8z = 3z + -1[2 + 4z + -2z] Combine like terms: 4z + -2z = 2z -11 + -8z = 3z + -1[2 + 2z] -11 + -8z = 3z + [2 * -1 + 2z * -1] -11 + -8z = 3z + [-2 + -2z] Reorder the terms: -11 + -8z = -2 + 3z + -2z Combine like terms: 3z + -2z = 1z -11 + -8z = -2 + 1z Solving -11 + -8z = -2 + 1z Solving for variable 'z'. Move all terms containing z to the left, all other terms to the right. Add '-1z' to each side of the equation. -11 + -8z + -1z = -2 + 1z + -1z Combine like terms: -8z + -1z = -9z -11 + -9z = -2 + 1z + -1z Combine like terms: 1z + -1z = 0 -11 + -9z = -2 + 0 -11 + -9z = -2 Add '11' to each side of the equation. -11 + 11 + -9z = -2 + 11 Combine like terms: -11 + 11 = 0 0 + -9z = -2 + 11 -9z = -2 + 11 Combine like terms: -2 + 11 = 9 -9z = 9 Divide each side by '-9'. z = -1 Simplifying z = -1
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