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Simplifying 2x4 + (2 + 2b) * x3 + (-10 + 2b) * x2 + (2 + -12b) * x + -12 = 0 Reorder the terms for easier multiplication: 2x4 + x3(2 + 2b) + (-10 + 2b) * x2 + (2 + -12b) * x + -12 = 0 2x4 + (2 * x3 + 2b * x3) + (-10 + 2b) * x2 + (2 + -12b) * x + -12 = 0 Reorder the terms: 2x4 + (2bx3 + 2x3) + (-10 + 2b) * x2 + (2 + -12b) * x + -12 = 0 2x4 + (2bx3 + 2x3) + (-10 + 2b) * x2 + (2 + -12b) * x + -12 = 0 Reorder the terms for easier multiplication: 2x4 + 2bx3 + 2x3 + x2(-10 + 2b) + (2 + -12b) * x + -12 = 0 2x4 + 2bx3 + 2x3 + (-10 * x2 + 2b * x2) + (2 + -12b) * x + -12 = 0 Reorder the terms: 2x4 + 2bx3 + 2x3 + (2bx2 + -10x2) + (2 + -12b) * x + -12 = 0 2x4 + 2bx3 + 2x3 + (2bx2 + -10x2) + (2 + -12b) * x + -12 = 0 Reorder the terms for easier multiplication: 2x4 + 2bx3 + 2x3 + 2bx2 + -10x2 + x(2 + -12b) + -12 = 0 2x4 + 2bx3 + 2x3 + 2bx2 + -10x2 + (2 * x + -12b * x) + -12 = 0 Reorder the terms: 2x4 + 2bx3 + 2x3 + 2bx2 + -10x2 + (-12bx + 2x) + -12 = 0 2x4 + 2bx3 + 2x3 + 2bx2 + -10x2 + (-12bx + 2x) + -12 = 0 Reorder the terms: -12 + -12bx + 2bx2 + 2bx3 + 2x + -10x2 + 2x3 + 2x4 = 0 Solving -12 + -12bx + 2bx2 + 2bx3 + 2x + -10x2 + 2x3 + 2x4 = 0 Solving for variable 'b'. Move all terms containing b to the left, all other terms to the right. Add '12' to each side of the equation. -12 + -12bx + 2bx2 + 2bx3 + 2x + -10x2 + 2x3 + 12 + 2x4 = 0 + 12 Reorder the terms: -12 + 12 + -12bx + 2bx2 + 2bx3 + 2x + -10x2 + 2x3 + 2x4 = 0 + 12 Combine like terms: -12 + 12 = 0 0 + -12bx + 2bx2 + 2bx3 + 2x + -10x2 + 2x3 + 2x4 = 0 + 12 -12bx + 2bx2 + 2bx3 + 2x + -10x2 + 2x3 + 2x4 = 0 + 12 Combine like terms: 0 + 12 = 12 -12bx + 2bx2 + 2bx3 + 2x + -10x2 + 2x3 + 2x4 = 12 Add '-2x' to each side of the equation. -12bx + 2bx2 + 2bx3 + 2x + -10x2 + 2x3 + -2x + 2x4 = 12 + -2x Reorder the terms: -12bx + 2bx2 + 2bx3 + 2x + -2x + -10x2 + 2x3 + 2x4 = 12 + -2x Combine like terms: 2x + -2x = 0 -12bx + 2bx2 + 2bx3 + 0 + -10x2 + 2x3 + 2x4 = 12 + -2x -12bx + 2bx2 + 2bx3 + -10x2 + 2x3 + 2x4 = 12 + -2x Add '10x2' to each side of the equation. -12bx + 2bx2 + 2bx3 + -10x2 + 2x3 + 10x2 + 2x4 = 12 + -2x + 10x2 Reorder the terms: -12bx + 2bx2 + 2bx3 + -10x2 + 10x2 + 2x3 + 2x4 = 12 + -2x + 10x2 Combine like terms: -10x2 + 10x2 = 0 -12bx + 2bx2 + 2bx3 + 0 + 2x3 + 2x4 = 12 + -2x + 10x2 -12bx + 2bx2 + 2bx3 + 2x3 + 2x4 = 12 + -2x + 10x2 Add '-2x3' to each side of the equation. -12bx + 2bx2 + 2bx3 + 2x3 + -2x3 + 2x4 = 12 + -2x + 10x2 + -2x3 Combine like terms: 2x3 + -2x3 = 0 -12bx + 2bx2 + 2bx3 + 0 + 2x4 = 12 + -2x + 10x2 + -2x3 -12bx + 2bx2 + 2bx3 + 2x4 = 12 + -2x + 10x2 + -2x3 Add '-2x4' to each side of the equation. -12bx + 2bx2 + 2bx3 + 2x4 + -2x4 = 12 + -2x + 10x2 + -2x3 + -2x4 Combine like terms: 2x4 + -2x4 = 0 -12bx + 2bx2 + 2bx3 + 0 = 12 + -2x + 10x2 + -2x3 + -2x4 -12bx + 2bx2 + 2bx3 = 12 + -2x + 10x2 + -2x3 + -2x4 Reorder the terms: -12 + -12bx + 2bx2 + 2bx3 + 2x + -10x2 + 2x3 + 2x4 = 12 + -2x + 10x2 + -2x3 + -2x4 + -12 + 2x + -10x2 + 2x3 + 2x4 Reorder the terms: -12 + -12bx + 2bx2 + 2bx3 + 2x + -10x2 + 2x3 + 2x4 = 12 + -12 + -2x + 2x + 10x2 + -10x2 + -2x3 + 2x3 + -2x4 + 2x4 Combine like terms: 12 + -12 = 0 -12 + -12bx + 2bx2 + 2bx3 + 2x + -10x2 + 2x3 + 2x4 = 0 + -2x + 2x + 10x2 + -10x2 + -2x3 + 2x3 + -2x4 + 2x4 -12 + -12bx + 2bx2 + 2bx3 + 2x + -10x2 + 2x3 + 2x4 = -2x + 2x + 10x2 + -10x2 + -2x3 + 2x3 + -2x4 + 2x4 Combine like terms: -2x + 2x = 0 -12 + -12bx + 2bx2 + 2bx3 + 2x + -10x2 + 2x3 + 2x4 = 0 + 10x2 + -10x2 + -2x3 + 2x3 + -2x4 + 2x4 -12 + -12bx + 2bx2 + 2bx3 + 2x + -10x2 + 2x3 + 2x4 = 10x2 + -10x2 + -2x3 + 2x3 + -2x4 + 2x4 Combine like terms: 10x2 + -10x2 = 0 -12 + -12bx + 2bx2 + 2bx3 + 2x + -10x2 + 2x3 + 2x4 = 0 + -2x3 + 2x3 + -2x4 + 2x4 -12 + -12bx + 2bx2 + 2bx3 + 2x + -10x2 + 2x3 + 2x4 = -2x3 + 2x3 + -2x4 + 2x4 Combine like terms: -2x3 + 2x3 = 0 -12 + -12bx + 2bx2 + 2bx3 + 2x + -10x2 + 2x3 + 2x4 = 0 + -2x4 + 2x4 -12 + -12bx + 2bx2 + 2bx3 + 2x + -10x2 + 2x3 + 2x4 = -2x4 + 2x4 Combine like terms: -2x4 + 2x4 = 0 -12 + -12bx + 2bx2 + 2bx3 + 2x + -10x2 + 2x3 + 2x4 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(-6 + -6bx + bx2 + bx3 + x + -5x2 + x3 + x4) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-6 + -6bx + bx2 + bx3 + x + -5x2 + x3 + x4)' equal to zero and attempt to solve: Simplifying -6 + -6bx + bx2 + bx3 + x + -5x2 + x3 + x4 = 0 Solving -6 + -6bx + bx2 + bx3 + x + -5x2 + x3 + x4 = 0 Move all terms containing b to the left, all other terms to the right. Add '6' to each side of the equation. -6 + -6bx + bx2 + bx3 + x + -5x2 + x3 + 6 + x4 = 0 + 6 Reorder the terms: -6 + 6 + -6bx + bx2 + bx3 + x + -5x2 + x3 + x4 = 0 + 6 Combine like terms: -6 + 6 = 0 0 + -6bx + bx2 + bx3 + x + -5x2 + x3 + x4 = 0 + 6 -6bx + bx2 + bx3 + x + -5x2 + x3 + x4 = 0 + 6 Combine like terms: 0 + 6 = 6 -6bx + bx2 + bx3 + x + -5x2 + x3 + x4 = 6 Add '-1x' to each side of the equation. -6bx + bx2 + bx3 + x + -5x2 + x3 + -1x + x4 = 6 + -1x Reorder the terms: -6bx + bx2 + bx3 + x + -1x + -5x2 + x3 + x4 = 6 + -1x Combine like terms: x + -1x = 0 -6bx + bx2 + bx3 + 0 + -5x2 + x3 + x4 = 6 + -1x -6bx + bx2 + bx3 + -5x2 + x3 + x4 = 6 + -1x Add '5x2' to each side of the equation. -6bx + bx2 + bx3 + -5x2 + x3 + 5x2 + x4 = 6 + -1x + 5x2 Reorder the terms: -6bx + bx2 + bx3 + -5x2 + 5x2 + x3 + x4 = 6 + -1x + 5x2 Combine like terms: -5x2 + 5x2 = 0 -6bx + bx2 + bx3 + 0 + x3 + x4 = 6 + -1x + 5x2 -6bx + bx2 + bx3 + x3 + x4 = 6 + -1x + 5x2 Add '-1x3' to each side of the equation. -6bx + bx2 + bx3 + x3 + -1x3 + x4 = 6 + -1x + 5x2 + -1x3 Combine like terms: x3 + -1x3 = 0 -6bx + bx2 + bx3 + 0 + x4 = 6 + -1x + 5x2 + -1x3 -6bx + bx2 + bx3 + x4 = 6 + -1x + 5x2 + -1x3 Add '-1x4' to each side of the equation. -6bx + bx2 + bx3 + x4 + -1x4 = 6 + -1x + 5x2 + -1x3 + -1x4 Combine like terms: x4 + -1x4 = 0 -6bx + bx2 + bx3 + 0 = 6 + -1x + 5x2 + -1x3 + -1x4 -6bx + bx2 + bx3 = 6 + -1x + 5x2 + -1x3 + -1x4 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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