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Simplifying (x3 + 9x2 + 6x + -16) = [(x + y)(x + 2)(x + 8)] Reorder the terms: (-16 + 6x + 9x2 + x3) = [(x + y)(x + 2)(x + 8)] Remove parenthesis around (-16 + 6x + 9x2 + x3) -16 + 6x + 9x2 + x3 = [(x + y)(x + 2)(x + 8)] Reorder the terms: -16 + 6x + 9x2 + x3 = [(x + y)(2 + x)(x + 8)] Reorder the terms: -16 + 6x + 9x2 + x3 = [(x + y)(2 + x)(8 + x)] Multiply (x + y) * (2 + x) -16 + 6x + 9x2 + x3 = [(x(2 + x) + y(2 + x))(8 + x)] -16 + 6x + 9x2 + x3 = [((2 * x + x * x) + y(2 + x))(8 + x)] -16 + 6x + 9x2 + x3 = [((2x + x2) + y(2 + x))(8 + x)] -16 + 6x + 9x2 + x3 = [(2x + x2 + (2 * y + x * y))(8 + x)] Reorder the terms: -16 + 6x + 9x2 + x3 = [(2x + x2 + (xy + 2y))(8 + x)] -16 + 6x + 9x2 + x3 = [(2x + x2 + (xy + 2y))(8 + x)] Reorder the terms: -16 + 6x + 9x2 + x3 = [(2x + xy + x2 + 2y)(8 + x)] -16 + 6x + 9x2 + x3 = [(2x + xy + x2 + 2y)(8 + x)] Multiply (2x + xy + x2 + 2y) * (8 + x) -16 + 6x + 9x2 + x3 = [(2x * (8 + x) + xy(8 + x) + x2(8 + x) + 2y * (8 + x))] -16 + 6x + 9x2 + x3 = [((8 * 2x + x * 2x) + xy(8 + x) + x2(8 + x) + 2y * (8 + x))] -16 + 6x + 9x2 + x3 = [((16x + 2x2) + xy(8 + x) + x2(8 + x) + 2y * (8 + x))] -16 + 6x + 9x2 + x3 = [(16x + 2x2 + (8 * xy + x * xy) + x2(8 + x) + 2y * (8 + x))] -16 + 6x + 9x2 + x3 = [(16x + 2x2 + (8xy + x2y) + x2(8 + x) + 2y * (8 + x))] -16 + 6x + 9x2 + x3 = [(16x + 2x2 + 8xy + x2y + (8 * x2 + x * x2) + 2y * (8 + x))] -16 + 6x + 9x2 + x3 = [(16x + 2x2 + 8xy + x2y + (8x2 + x3) + 2y * (8 + x))] -16 + 6x + 9x2 + x3 = [(16x + 2x2 + 8xy + x2y + 8x2 + x3 + (8 * 2y + x * 2y))] Reorder the terms: -16 + 6x + 9x2 + x3 = [(16x + 2x2 + 8xy + x2y + 8x2 + x3 + (2xy + 16y))] -16 + 6x + 9x2 + x3 = [(16x + 2x2 + 8xy + x2y + 8x2 + x3 + (2xy + 16y))] Reorder the terms: -16 + 6x + 9x2 + x3 = [(16x + 8xy + 2xy + 2x2 + 8x2 + x2y + x3 + 16y)] Combine like terms: 8xy + 2xy = 10xy -16 + 6x + 9x2 + x3 = [(16x + 10xy + 2x2 + 8x2 + x2y + x3 + 16y)] Combine like terms: 2x2 + 8x2 = 10x2 -16 + 6x + 9x2 + x3 = [(16x + 10xy + 10x2 + x2y + x3 + 16y)] -16 + 6x + 9x2 + x3 = [16x + 10xy + 10x2 + x2y + x3 + 16y] Remove brackets around [16x + 10xy + 10x2 + x2y + x3 + 16y] -16 + 6x + 9x2 + x3 = 16x + 10xy + 10x2 + x2y + x3 + 16y Add '-1x3' to each side of the equation. -16 + 6x + 9x2 + x3 + -1x3 = 16x + 10xy + 10x2 + x2y + x3 + -1x3 + 16y Combine like terms: x3 + -1x3 = 0 -16 + 6x + 9x2 + 0 = 16x + 10xy + 10x2 + x2y + x3 + -1x3 + 16y -16 + 6x + 9x2 = 16x + 10xy + 10x2 + x2y + x3 + -1x3 + 16y Combine like terms: x3 + -1x3 = 0 -16 + 6x + 9x2 = 16x + 10xy + 10x2 + x2y + 0 + 16y -16 + 6x + 9x2 = 16x + 10xy + 10x2 + x2y + 16y Solving -16 + 6x + 9x2 = 16x + 10xy + 10x2 + x2y + 16y Solving for variable 'x'. Reorder the terms: -16 + 6x + -16x + -10xy + 9x2 + -10x2 + -1x2y + -16y = 16x + 10xy + 10x2 + x2y + 16y + -16x + -10xy + -10x2 + -1x2y + -16y Combine like terms: 6x + -16x = -10x -16 + -10x + -10xy + 9x2 + -10x2 + -1x2y + -16y = 16x + 10xy + 10x2 + x2y + 16y + -16x + -10xy + -10x2 + -1x2y + -16y Combine like terms: 9x2 + -10x2 = -1x2 -16 + -10x + -10xy + -1x2 + -1x2y + -16y = 16x + 10xy + 10x2 + x2y + 16y + -16x + -10xy + -10x2 + -1x2y + -16y Reorder the terms: -16 + -10x + -10xy + -1x2 + -1x2y + -16y = 16x + -16x + 10xy + -10xy + 10x2 + -10x2 + x2y + -1x2y + 16y + -16y Combine like terms: 16x + -16x = 0 -16 + -10x + -10xy + -1x2 + -1x2y + -16y = 0 + 10xy + -10xy + 10x2 + -10x2 + x2y + -1x2y + 16y + -16y -16 + -10x + -10xy + -1x2 + -1x2y + -16y = 10xy + -10xy + 10x2 + -10x2 + x2y + -1x2y + 16y + -16y Combine like terms: 10xy + -10xy = 0 -16 + -10x + -10xy + -1x2 + -1x2y + -16y = 0 + 10x2 + -10x2 + x2y + -1x2y + 16y + -16y -16 + -10x + -10xy + -1x2 + -1x2y + -16y = 10x2 + -10x2 + x2y + -1x2y + 16y + -16y Combine like terms: 10x2 + -10x2 = 0 -16 + -10x + -10xy + -1x2 + -1x2y + -16y = 0 + x2y + -1x2y + 16y + -16y -16 + -10x + -10xy + -1x2 + -1x2y + -16y = x2y + -1x2y + 16y + -16y Combine like terms: x2y + -1x2y = 0 -16 + -10x + -10xy + -1x2 + -1x2y + -16y = 0 + 16y + -16y -16 + -10x + -10xy + -1x2 + -1x2y + -16y = 16y + -16y Combine like terms: 16y + -16y = 0 -16 + -10x + -10xy + -1x2 + -1x2y + -16y = 0 Factor out the Greatest Common Factor (GCF), '-1'. -1(16 + 10x + 10xy + x2 + x2y + 16y) = 0 Ignore the factor -1.Subproblem 1
Set the factor '(16 + 10x + 10xy + x2 + x2y + 16y)' equal to zero and attempt to solve: Simplifying 16 + 10x + 10xy + x2 + x2y + 16y = 0 Solving 16 + 10x + 10xy + x2 + x2y + 16y = 0 The solution to this equation could not be determined. This subproblem is being ignored because a solution could not be determined. The solution to this equation could not be determined.
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