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Simplifying (X + 1)(X + -1)(X + -2) + -1(X2 + 7X)(X + -4) + -2 = 2X Reorder the terms: (1 + X)(X + -1)(X + -2) + -1(X2 + 7X)(X + -4) + -2 = 2X Reorder the terms: (1 + X)(-1 + X)(X + -2) + -1(X2 + 7X)(X + -4) + -2 = 2X Reorder the terms: (1 + X)(-1 + X)(-2 + X) + -1(X2 + 7X)(X + -4) + -2 = 2X Multiply (1 + X) * (-1 + X) (1(-1 + X) + X(-1 + X))(-2 + X) + -1(X2 + 7X)(X + -4) + -2 = 2X ((-1 * 1 + X * 1) + X(-1 + X))(-2 + X) + -1(X2 + 7X)(X + -4) + -2 = 2X ((-1 + 1X) + X(-1 + X))(-2 + X) + -1(X2 + 7X)(X + -4) + -2 = 2X (-1 + 1X + (-1 * X + X * X))(-2 + X) + -1(X2 + 7X)(X + -4) + -2 = 2X (-1 + 1X + (-1X + X2))(-2 + X) + -1(X2 + 7X)(X + -4) + -2 = 2X Combine like terms: 1X + -1X = 0 (-1 + 0 + X2)(-2 + X) + -1(X2 + 7X)(X + -4) + -2 = 2X (-1 + X2)(-2 + X) + -1(X2 + 7X)(X + -4) + -2 = 2X Multiply (-1 + X2) * (-2 + X) (-1(-2 + X) + X2(-2 + X)) + -1(X2 + 7X)(X + -4) + -2 = 2X ((-2 * -1 + X * -1) + X2(-2 + X)) + -1(X2 + 7X)(X + -4) + -2 = 2X ((2 + -1X) + X2(-2 + X)) + -1(X2 + 7X)(X + -4) + -2 = 2X (2 + -1X + (-2 * X2 + X * X2)) + -1(X2 + 7X)(X + -4) + -2 = 2X (2 + -1X + (-2X2 + X3)) + -1(X2 + 7X)(X + -4) + -2 = 2X (2 + -1X + -2X2 + X3) + -1(X2 + 7X)(X + -4) + -2 = 2X Reorder the terms: 2 + -1X + -2X2 + X3 + -1(7X + X2)(X + -4) + -2 = 2X Reorder the terms: 2 + -1X + -2X2 + X3 + -1(7X + X2)(-4 + X) + -2 = 2X Multiply (7X + X2) * (-4 + X) 2 + -1X + -2X2 + X3 + -1(7X * (-4 + X) + X2(-4 + X)) + -2 = 2X 2 + -1X + -2X2 + X3 + -1((-4 * 7X + X * 7X) + X2(-4 + X)) + -2 = 2X 2 + -1X + -2X2 + X3 + -1((-28X + 7X2) + X2(-4 + X)) + -2 = 2X 2 + -1X + -2X2 + X3 + -1(-28X + 7X2 + (-4 * X2 + X * X2)) + -2 = 2X 2 + -1X + -2X2 + X3 + -1(-28X + 7X2 + (-4X2 + X3)) + -2 = 2X Combine like terms: 7X2 + -4X2 = 3X2 2 + -1X + -2X2 + X3 + -1(-28X + 3X2 + X3) + -2 = 2X 2 + -1X + -2X2 + X3 + (-28X * -1 + 3X2 * -1 + X3 * -1) + -2 = 2X 2 + -1X + -2X2 + X3 + (28X + -3X2 + -1X3) + -2 = 2X Reorder the terms: 2 + -2 + -1X + 28X + -2X2 + -3X2 + X3 + -1X3 = 2X Combine like terms: 2 + -2 = 0 0 + -1X + 28X + -2X2 + -3X2 + X3 + -1X3 = 2X -1X + 28X + -2X2 + -3X2 + X3 + -1X3 = 2X Combine like terms: -1X + 28X = 27X 27X + -2X2 + -3X2 + X3 + -1X3 = 2X Combine like terms: -2X2 + -3X2 = -5X2 27X + -5X2 + X3 + -1X3 = 2X Combine like terms: X3 + -1X3 = 0 27X + -5X2 + 0 = 2X 27X + -5X2 = 2X Solving 27X + -5X2 = 2X Solving for variable 'X'. Reorder the terms: 27X + -2X + -5X2 = 2X + -2X Combine like terms: 27X + -2X = 25X 25X + -5X2 = 2X + -2X Combine like terms: 2X + -2X = 0 25X + -5X2 = 0 Factor out the Greatest Common Factor (GCF), '5X'. 5X(5 + -1X) = 0 Ignore the factor 5.Subproblem 1
Set the factor 'X' equal to zero and attempt to solve: Simplifying X = 0 Solving X = 0 Move all terms containing X to the left, all other terms to the right. Simplifying X = 0Subproblem 2
Set the factor '(5 + -1X)' equal to zero and attempt to solve: Simplifying 5 + -1X = 0 Solving 5 + -1X = 0 Move all terms containing X to the left, all other terms to the right. Add '-5' to each side of the equation. 5 + -5 + -1X = 0 + -5 Combine like terms: 5 + -5 = 0 0 + -1X = 0 + -5 -1X = 0 + -5 Combine like terms: 0 + -5 = -5 -1X = -5 Divide each side by '-1'. X = 5 Simplifying X = 5Solution
X = {0, 5}
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