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Simplifying (x2 + -3)(x2 + x + 1) = x4 + x3 + -2x3 + -3x + -3 Reorder the terms: (-3 + x2)(x2 + x + 1) = x4 + x3 + -2x3 + -3x + -3 Reorder the terms: (-3 + x2)(1 + x + x2) = x4 + x3 + -2x3 + -3x + -3 Multiply (-3 + x2) * (1 + x + x2) (-3(1 + x + x2) + x2(1 + x + x2)) = x4 + x3 + -2x3 + -3x + -3 ((1 * -3 + x * -3 + x2 * -3) + x2(1 + x + x2)) = x4 + x3 + -2x3 + -3x + -3 ((-3 + -3x + -3x2) + x2(1 + x + x2)) = x4 + x3 + -2x3 + -3x + -3 (-3 + -3x + -3x2 + (1 * x2 + x * x2 + x2 * x2)) = x4 + x3 + -2x3 + -3x + -3 (-3 + -3x + -3x2 + (1x2 + x3 + x4)) = x4 + x3 + -2x3 + -3x + -3 Combine like terms: -3x2 + 1x2 = -2x2 (-3 + -3x + -2x2 + x3 + x4) = x4 + x3 + -2x3 + -3x + -3 Reorder the terms: -3 + -3x + -2x2 + x3 + x4 = -3 + -3x + x3 + -2x3 + x4 Combine like terms: x3 + -2x3 = -1x3 -3 + -3x + -2x2 + x3 + x4 = -3 + -3x + -1x3 + x4 Add '3' to each side of the equation. -3 + -3x + -2x2 + x3 + 3 + x4 = -3 + -3x + -1x3 + 3 + x4 Reorder the terms: -3 + 3 + -3x + -2x2 + x3 + x4 = -3 + -3x + -1x3 + 3 + x4 Combine like terms: -3 + 3 = 0 0 + -3x + -2x2 + x3 + x4 = -3 + -3x + -1x3 + 3 + x4 -3x + -2x2 + x3 + x4 = -3 + -3x + -1x3 + 3 + x4 Reorder the terms: -3x + -2x2 + x3 + x4 = -3 + 3 + -3x + -1x3 + x4 Combine like terms: -3 + 3 = 0 -3x + -2x2 + x3 + x4 = 0 + -3x + -1x3 + x4 -3x + -2x2 + x3 + x4 = -3x + -1x3 + x4 Add '3x' to each side of the equation. -3x + -2x2 + x3 + 3x + x4 = -3x + -1x3 + 3x + x4 Reorder the terms: -3x + 3x + -2x2 + x3 + x4 = -3x + -1x3 + 3x + x4 Combine like terms: -3x + 3x = 0 0 + -2x2 + x3 + x4 = -3x + -1x3 + 3x + x4 -2x2 + x3 + x4 = -3x + -1x3 + 3x + x4 Reorder the terms: -2x2 + x3 + x4 = -3x + 3x + -1x3 + x4 Combine like terms: -3x + 3x = 0 -2x2 + x3 + x4 = 0 + -1x3 + x4 -2x2 + x3 + x4 = -1x3 + x4 Add '-1x4' to each side of the equation. -2x2 + x3 + x4 + -1x4 = -1x3 + x4 + -1x4 Combine like terms: x4 + -1x4 = 0 -2x2 + x3 + 0 = -1x3 + x4 + -1x4 -2x2 + x3 = -1x3 + x4 + -1x4 Combine like terms: x4 + -1x4 = 0 -2x2 + x3 = -1x3 + 0 -2x2 + x3 = -1x3 Solving -2x2 + x3 = -1x3 Solving for variable 'x'. Combine like terms: x3 + x3 = 2x3 -2x2 + 2x3 = -1x3 + x3 Combine like terms: -1x3 + x3 = 0 -2x2 + 2x3 = 0 Factor out the Greatest Common Factor (GCF), '2x2'. 2x2(-1 + x) = 0 Ignore the factor 2.Subproblem 1
Set the factor 'x2' equal to zero and attempt to solve: Simplifying x2 = 0 Solving x2 = 0 Move all terms containing x to the left, all other terms to the right. Simplifying x2 = 0 Take the square root of each side: x = {0}Subproblem 2
Set the factor '(-1 + x)' equal to zero and attempt to solve: Simplifying -1 + x = 0 Solving -1 + x = 0 Move all terms containing x to the left, all other terms to the right. Add '1' to each side of the equation. -1 + 1 + x = 0 + 1 Combine like terms: -1 + 1 = 0 0 + x = 0 + 1 x = 0 + 1 Combine like terms: 0 + 1 = 1 x = 1 Simplifying x = 1Solution
x = {0, 1}
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