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Simplifying 4(ax2 + -5x + 3) = 8x2 + bx + c Reorder the terms: 4(3 + ax2 + -5x) = 8x2 + bx + c (3 * 4 + ax2 * 4 + -5x * 4) = 8x2 + bx + c (12 + 4ax2 + -20x) = 8x2 + bx + c Reorder the terms: 12 + 4ax2 + -20x = bx + c + 8x2 Solving 12 + 4ax2 + -20x = bx + c + 8x2 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '-12' to each side of the equation. 12 + 4ax2 + -12 + -20x = bx + c + -12 + 8x2 Reorder the terms: 12 + -12 + 4ax2 + -20x = bx + c + -12 + 8x2 Combine like terms: 12 + -12 = 0 0 + 4ax2 + -20x = bx + c + -12 + 8x2 4ax2 + -20x = bx + c + -12 + 8x2 Reorder the terms: 4ax2 + -20x = -12 + bx + c + 8x2 Add '20x' to each side of the equation. 4ax2 + -20x + 20x = -12 + bx + c + 20x + 8x2 Combine like terms: -20x + 20x = 0 4ax2 + 0 = -12 + bx + c + 20x + 8x2 4ax2 = -12 + bx + c + 20x + 8x2 Divide each side by '4x2'. a = -3x-2 + 0.25bx-1 + 0.25cx-2 + 5x-1 + 2 Simplifying a = -3x-2 + 0.25bx-1 + 0.25cx-2 + 5x-1 + 2 Reorder the terms: a = 2 + 0.25bx-1 + 0.25cx-2 + -3x-2 + 5x-1
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