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Simplifying (x + -1)(x + -2)(x + -4)(x + -5) = 40 Reorder the terms: (-1 + x)(x + -2)(x + -4)(x + -5) = 40 Reorder the terms: (-1 + x)(-2 + x)(x + -4)(x + -5) = 40 Reorder the terms: (-1 + x)(-2 + x)(-4 + x)(x + -5) = 40 Reorder the terms: (-1 + x)(-2 + x)(-4 + x)(-5 + x) = 40 Multiply (-1 + x) * (-2 + x) (-1(-2 + x) + x(-2 + x))(-4 + x)(-5 + x) = 40 ((-2 * -1 + x * -1) + x(-2 + x))(-4 + x)(-5 + x) = 40 ((2 + -1x) + x(-2 + x))(-4 + x)(-5 + x) = 40 (2 + -1x + (-2 * x + x * x))(-4 + x)(-5 + x) = 40 (2 + -1x + (-2x + x2))(-4 + x)(-5 + x) = 40 Combine like terms: -1x + -2x = -3x (2 + -3x + x2)(-4 + x)(-5 + x) = 40 Multiply (2 + -3x + x2) * (-4 + x) (2(-4 + x) + -3x * (-4 + x) + x2(-4 + x))(-5 + x) = 40 ((-4 * 2 + x * 2) + -3x * (-4 + x) + x2(-4 + x))(-5 + x) = 40 ((-8 + 2x) + -3x * (-4 + x) + x2(-4 + x))(-5 + x) = 40 (-8 + 2x + (-4 * -3x + x * -3x) + x2(-4 + x))(-5 + x) = 40 (-8 + 2x + (12x + -3x2) + x2(-4 + x))(-5 + x) = 40 (-8 + 2x + 12x + -3x2 + (-4 * x2 + x * x2))(-5 + x) = 40 (-8 + 2x + 12x + -3x2 + (-4x2 + x3))(-5 + x) = 40 Combine like terms: 2x + 12x = 14x (-8 + 14x + -3x2 + -4x2 + x3)(-5 + x) = 40 Combine like terms: -3x2 + -4x2 = -7x2 (-8 + 14x + -7x2 + x3)(-5 + x) = 40 Multiply (-8 + 14x + -7x2 + x3) * (-5 + x) (-8(-5 + x) + 14x * (-5 + x) + -7x2 * (-5 + x) + x3(-5 + x)) = 40 ((-5 * -8 + x * -8) + 14x * (-5 + x) + -7x2 * (-5 + x) + x3(-5 + x)) = 40 ((40 + -8x) + 14x * (-5 + x) + -7x2 * (-5 + x) + x3(-5 + x)) = 40 (40 + -8x + (-5 * 14x + x * 14x) + -7x2 * (-5 + x) + x3(-5 + x)) = 40 (40 + -8x + (-70x + 14x2) + -7x2 * (-5 + x) + x3(-5 + x)) = 40 (40 + -8x + -70x + 14x2 + (-5 * -7x2 + x * -7x2) + x3(-5 + x)) = 40 (40 + -8x + -70x + 14x2 + (35x2 + -7x3) + x3(-5 + x)) = 40 (40 + -8x + -70x + 14x2 + 35x2 + -7x3 + (-5 * x3 + x * x3)) = 40 (40 + -8x + -70x + 14x2 + 35x2 + -7x3 + (-5x3 + x4)) = 40 Combine like terms: -8x + -70x = -78x (40 + -78x + 14x2 + 35x2 + -7x3 + -5x3 + x4) = 40 Combine like terms: 14x2 + 35x2 = 49x2 (40 + -78x + 49x2 + -7x3 + -5x3 + x4) = 40 Combine like terms: -7x3 + -5x3 = -12x3 (40 + -78x + 49x2 + -12x3 + x4) = 40 Add '-40' to each side of the equation. 40 + -78x + 49x2 + -12x3 + -40 + x4 = 40 + -40 Reorder the terms: 40 + -40 + -78x + 49x2 + -12x3 + x4 = 40 + -40 Combine like terms: 40 + -40 = 0 0 + -78x + 49x2 + -12x3 + x4 = 40 + -40 -78x + 49x2 + -12x3 + x4 = 40 + -40 Combine like terms: 40 + -40 = 0 -78x + 49x2 + -12x3 + x4 = 0 Solving -78x + 49x2 + -12x3 + x4 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), 'x'. x(-78 + 49x + -12x2 + x3) = 0Subproblem 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 '(-78 + 49x + -12x2 + x3)' equal to zero and attempt to solve: Simplifying -78 + 49x + -12x2 + x3 = 0 Solving -78 + 49x + -12x2 + x3 = 0 The solution to this equation could not be determined. This subproblem is being ignored because a solution could not be determined.Solution
x = {0}
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