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Simplifying cx2 + ax3 + -3x2 + 2bx + -2 + -2x3 + 5x + 4d = x2 + x + -6 Reorder the terms: -2 + ax3 + 2bx + cx2 + 4d + 5x + -3x2 + -2x3 = x2 + x + -6 Reorder the terms: -2 + ax3 + 2bx + cx2 + 4d + 5x + -3x2 + -2x3 = -6 + x + x2 Solving -2 + ax3 + 2bx + cx2 + 4d + 5x + -3x2 + -2x3 = -6 + x + x2 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '2' to each side of the equation. -2 + ax3 + 2bx + cx2 + 4d + 5x + -3x2 + 2 + -2x3 = -6 + x + 2 + x2 Reorder the terms: -2 + 2 + ax3 + 2bx + cx2 + 4d + 5x + -3x2 + -2x3 = -6 + x + 2 + x2 Combine like terms: -2 + 2 = 0 0 + ax3 + 2bx + cx2 + 4d + 5x + -3x2 + -2x3 = -6 + x + 2 + x2 ax3 + 2bx + cx2 + 4d + 5x + -3x2 + -2x3 = -6 + x + 2 + x2 Reorder the terms: ax3 + 2bx + cx2 + 4d + 5x + -3x2 + -2x3 = -6 + 2 + x + x2 Combine like terms: -6 + 2 = -4 ax3 + 2bx + cx2 + 4d + 5x + -3x2 + -2x3 = -4 + x + x2 Add '-2bx' to each side of the equation. ax3 + 2bx + cx2 + 4d + 5x + -3x2 + -2bx + -2x3 = -4 + x + -2bx + x2 Reorder the terms: ax3 + 2bx + -2bx + cx2 + 4d + 5x + -3x2 + -2x3 = -4 + x + -2bx + x2 Combine like terms: 2bx + -2bx = 0 ax3 + 0 + cx2 + 4d + 5x + -3x2 + -2x3 = -4 + x + -2bx + x2 ax3 + cx2 + 4d + 5x + -3x2 + -2x3 = -4 + x + -2bx + x2 Reorder the terms: ax3 + cx2 + 4d + 5x + -3x2 + -2x3 = -4 + -2bx + x + x2 Add '-1cx2' to each side of the equation. ax3 + cx2 + 4d + 5x + -3x2 + -1cx2 + -2x3 = -4 + -2bx + x + -1cx2 + x2 Reorder the terms: ax3 + cx2 + -1cx2 + 4d + 5x + -3x2 + -2x3 = -4 + -2bx + x + -1cx2 + x2 Combine like terms: cx2 + -1cx2 = 0 ax3 + 0 + 4d + 5x + -3x2 + -2x3 = -4 + -2bx + x + -1cx2 + x2 ax3 + 4d + 5x + -3x2 + -2x3 = -4 + -2bx + x + -1cx2 + x2 Reorder the terms: ax3 + 4d + 5x + -3x2 + -2x3 = -4 + -2bx + -1cx2 + x + x2 Add '-4d' to each side of the equation. ax3 + 4d + 5x + -3x2 + -4d + -2x3 = -4 + -2bx + -1cx2 + x + -4d + x2 Reorder the terms: ax3 + 4d + -4d + 5x + -3x2 + -2x3 = -4 + -2bx + -1cx2 + x + -4d + x2 Combine like terms: 4d + -4d = 0 ax3 + 0 + 5x + -3x2 + -2x3 = -4 + -2bx + -1cx2 + x + -4d + x2 ax3 + 5x + -3x2 + -2x3 = -4 + -2bx + -1cx2 + x + -4d + x2 Reorder the terms: ax3 + 5x + -3x2 + -2x3 = -4 + -2bx + -1cx2 + -4d + x + x2 Add '-5x' to each side of the equation. ax3 + 5x + -3x2 + -5x + -2x3 = -4 + -2bx + -1cx2 + -4d + x + -5x + x2 Reorder the terms: ax3 + 5x + -5x + -3x2 + -2x3 = -4 + -2bx + -1cx2 + -4d + x + -5x + x2 Combine like terms: 5x + -5x = 0 ax3 + 0 + -3x2 + -2x3 = -4 + -2bx + -1cx2 + -4d + x + -5x + x2 ax3 + -3x2 + -2x3 = -4 + -2bx + -1cx2 + -4d + x + -5x + x2 Combine like terms: x + -5x = -4x ax3 + -3x2 + -2x3 = -4 + -2bx + -1cx2 + -4d + -4x + x2 Add '3x2' to each side of the equation. ax3 + -3x2 + 3x2 + -2x3 = -4 + -2bx + -1cx2 + -4d + -4x + x2 + 3x2 Combine like terms: -3x2 + 3x2 = 0 ax3 + 0 + -2x3 = -4 + -2bx + -1cx2 + -4d + -4x + x2 + 3x2 ax3 + -2x3 = -4 + -2bx + -1cx2 + -4d + -4x + x2 + 3x2 Combine like terms: x2 + 3x2 = 4x2 ax3 + -2x3 = -4 + -2bx + -1cx2 + -4d + -4x + 4x2 Add '2x3' to each side of the equation. ax3 + -2x3 + 2x3 = -4 + -2bx + -1cx2 + -4d + -4x + 4x2 + 2x3 Combine like terms: -2x3 + 2x3 = 0 ax3 + 0 = -4 + -2bx + -1cx2 + -4d + -4x + 4x2 + 2x3 ax3 = -4 + -2bx + -1cx2 + -4d + -4x + 4x2 + 2x3 Divide each side by 'x3'. a = -4x-3 + -2bx-2 + -1cx-1 + -4dx-3 + -4x-2 + 4x-1 + 2 Simplifying a = -4x-3 + -2bx-2 + -1cx-1 + -4dx-3 + -4x-2 + 4x-1 + 2 Reorder the terms: a = 2 + -2bx-2 + -1cx-1 + -4dx-3 + -4x-3 + -4x-2 + 4x-1
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