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Simplifying (-2 + -1x)((10 + -1x)(-4 + -1x) + 48) + 4((8(-4 + -1x)) + 48) + 4(8 * 6 + -1(10 + -1x) * 6) = 0 Multiply (10 + -1x) * (-4 + -1x) (-2 + -1x)((10(-4 + -1x) + -1x * (-4 + -1x)) + 48) + 4((8(-4 + -1x)) + 48) + 4(8 * 6 + -1(10 + -1x) * 6) = 0 (-2 + -1x)(((-4 * 10 + -1x * 10) + -1x * (-4 + -1x)) + 48) + 4((8(-4 + -1x)) + 48) + 4(8 * 6 + -1(10 + -1x) * 6) = 0 (-2 + -1x)(((-40 + -10x) + -1x * (-4 + -1x)) + 48) + 4((8(-4 + -1x)) + 48) + 4(8 * 6 + -1(10 + -1x) * 6) = 0 (-2 + -1x)((-40 + -10x + (-4 * -1x + -1x * -1x)) + 48) + 4((8(-4 + -1x)) + 48) + 4(8 * 6 + -1(10 + -1x) * 6) = 0 (-2 + -1x)((-40 + -10x + (4x + 1x2)) + 48) + 4((8(-4 + -1x)) + 48) + 4(8 * 6 + -1(10 + -1x) * 6) = 0 Combine like terms: -10x + 4x = -6x (-2 + -1x)((-40 + -6x + 1x2) + 48) + 4((8(-4 + -1x)) + 48) + 4(8 * 6 + -1(10 + -1x) * 6) = 0 Reorder the terms: (-2 + -1x)(-40 + 48 + -6x + 1x2) + 4((8(-4 + -1x)) + 48) + 4(8 * 6 + -1(10 + -1x) * 6) = 0 Combine like terms: -40 + 48 = 8 (-2 + -1x)(8 + -6x + 1x2) + 4((8(-4 + -1x)) + 48) + 4(8 * 6 + -1(10 + -1x) * 6) = 0 Multiply (-2 + -1x) * (8 + -6x + 1x2) (-2(8 + -6x + 1x2) + -1x * (8 + -6x + 1x2)) + 4((8(-4 + -1x)) + 48) + 4(8 * 6 + -1(10 + -1x) * 6) = 0 ((8 * -2 + -6x * -2 + 1x2 * -2) + -1x * (8 + -6x + 1x2)) + 4((8(-4 + -1x)) + 48) + 4(8 * 6 + -1(10 + -1x) * 6) = 0 ((-16 + 12x + -2x2) + -1x * (8 + -6x + 1x2)) + 4((8(-4 + -1x)) + 48) + 4(8 * 6 + -1(10 + -1x) * 6) = 0 (-16 + 12x + -2x2 + (8 * -1x + -6x * -1x + 1x2 * -1x)) + 4((8(-4 + -1x)) + 48) + 4(8 * 6 + -1(10 + -1x) * 6) = 0 (-16 + 12x + -2x2 + (-8x + 6x2 + -1x3)) + 4((8(-4 + -1x)) + 48) + 4(8 * 6 + -1(10 + -1x) * 6) = 0 Reorder the terms: (-16 + 12x + -8x + -2x2 + 6x2 + -1x3) + 4((8(-4 + -1x)) + 48) + 4(8 * 6 + -1(10 + -1x) * 6) = 0 Combine like terms: 12x + -8x = 4x (-16 + 4x + -2x2 + 6x2 + -1x3) + 4((8(-4 + -1x)) + 48) + 4(8 * 6 + -1(10 + -1x) * 6) = 0 Combine like terms: -2x2 + 6x2 = 4x2 (-16 + 4x + 4x2 + -1x3) + 4((8(-4 + -1x)) + 48) + 4(8 * 6 + -1(10 + -1x) * 6) = 0 -16 + 4x + 4x2 + -1x3 + 4(((-4 * 8 + -1x * 8)) + 48) + 4(8 * 6 + -1(10 + -1x) * 6) = 0 -16 + 4x + 4x2 + -1x3 + 4(((-32 + -8x)) + 48) + 4(8 * 6 + -1(10 + -1x) * 6) = 0 -16 + 4x + 4x2 + -1x3 + 4((-32 + -8x) + 48) + 4(8 * 6 + -1(10 + -1x) * 6) = 0 Remove parenthesis around (-32 + -8x) -16 + 4x + 4x2 + -1x3 + 4(-32 + -8x + 48) + 4(8 * 6 + -1(10 + -1x) * 6) = 0 Reorder the terms: -16 + 4x + 4x2 + -1x3 + 4(-32 + 48 + -8x) + 4(8 * 6 + -1(10 + -1x) * 6) = 0 Combine like terms: -32 + 48 = 16 -16 + 4x + 4x2 + -1x3 + 4(16 + -8x) + 4(8 * 6 + -1(10 + -1x) * 6) = 0 -16 + 4x + 4x2 + -1x3 + (16 * 4 + -8x * 4) + 4(8 * 6 + -1(10 + -1x) * 6) = 0 -16 + 4x + 4x2 + -1x3 + (64 + -32x) + 4(8 * 6 + -1(10 + -1x) * 6) = 0 Multiply 8 * 6 -16 + 4x + 4x2 + -1x3 + 64 + -32x + 4(48 + -1(10 + -1x) * 6) = 0 Reorder the terms for easier multiplication: -16 + 4x + 4x2 + -1x3 + 64 + -32x + 4(48 + -1 * 6(10 + -1x)) = 0 Multiply -1 * 6 -16 + 4x + 4x2 + -1x3 + 64 + -32x + 4(48 + -6(10 + -1x)) = 0 -16 + 4x + 4x2 + -1x3 + 64 + -32x + 4(48 + (10 * -6 + -1x * -6)) = 0 -16 + 4x + 4x2 + -1x3 + 64 + -32x + 4(48 + (-60 + 6x)) = 0 Combine like terms: 48 + -60 = -12 -16 + 4x + 4x2 + -1x3 + 64 + -32x + 4(-12 + 6x) = 0 -16 + 4x + 4x2 + -1x3 + 64 + -32x + (-12 * 4 + 6x * 4) = 0 -16 + 4x + 4x2 + -1x3 + 64 + -32x + (-48 + 24x) = 0 Reorder the terms: -16 + 64 + -48 + 4x + -32x + 24x + 4x2 + -1x3 = 0 Combine like terms: -16 + 64 = 48 48 + -48 + 4x + -32x + 24x + 4x2 + -1x3 = 0 Combine like terms: 48 + -48 = 0 0 + 4x + -32x + 24x + 4x2 + -1x3 = 0 4x + -32x + 24x + 4x2 + -1x3 = 0 Combine like terms: 4x + -32x = -28x -28x + 24x + 4x2 + -1x3 = 0 Combine like terms: -28x + 24x = -4x -4x + 4x2 + -1x3 = 0 Solving -4x + 4x2 + -1x3 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), 'x'. x(-4 + 4x + -1x2) = 0 Factor a trinomial. x((-2 + x)(2 + -1x)) = 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 '(-2 + x)' equal to zero and attempt to solve: Simplifying -2 + x = 0 Solving -2 + x = 0 Move all terms containing x to the left, all other terms to the right. Add '2' to each side of the equation. -2 + 2 + x = 0 + 2 Combine like terms: -2 + 2 = 0 0 + x = 0 + 2 x = 0 + 2 Combine like terms: 0 + 2 = 2 x = 2 Simplifying x = 2Subproblem 3
Set the factor '(2 + -1x)' equal to zero and attempt to solve: Simplifying 2 + -1x = 0 Solving 2 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + -1x = 0 + -2 Combine like terms: 2 + -2 = 0 0 + -1x = 0 + -2 -1x = 0 + -2 Combine like terms: 0 + -2 = -2 -1x = -2 Divide each side by '-1'. x = 2 Simplifying x = 2Solution
x = {0, 2, 2}
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