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Simplifying ax2 + bx + c = (2x + -3)(x + 5) Reorder the terms: ax2 + bx + c = (-3 + 2x)(x + 5) Reorder the terms: ax2 + bx + c = (-3 + 2x)(5 + x) Multiply (-3 + 2x) * (5 + x) ax2 + bx + c = (-3(5 + x) + 2x * (5 + x)) ax2 + bx + c = ((5 * -3 + x * -3) + 2x * (5 + x)) ax2 + bx + c = ((-15 + -3x) + 2x * (5 + x)) ax2 + bx + c = (-15 + -3x + (5 * 2x + x * 2x)) ax2 + bx + c = (-15 + -3x + (10x + 2x2)) Combine like terms: -3x + 10x = 7x ax2 + bx + c = (-15 + 7x + 2x2) Solving ax2 + bx + c = -15 + 7x + 2x2 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '-1bx' to each side of the equation. ax2 + bx + -1bx + c = -15 + 7x + -1bx + 2x2 Combine like terms: bx + -1bx = 0 ax2 + 0 + c = -15 + 7x + -1bx + 2x2 ax2 + c = -15 + 7x + -1bx + 2x2 Reorder the terms: ax2 + c = -15 + -1bx + 7x + 2x2 Add '-1c' to each side of the equation. ax2 + c + -1c = -15 + -1bx + 7x + -1c + 2x2 Combine like terms: c + -1c = 0 ax2 + 0 = -15 + -1bx + 7x + -1c + 2x2 ax2 = -15 + -1bx + 7x + -1c + 2x2 Reorder the terms: ax2 = -15 + -1bx + -1c + 7x + 2x2 Divide each side by 'x2'. a = -15x-2 + -1bx-1 + -1cx-2 + 7x-1 + 2 Simplifying a = -15x-2 + -1bx-1 + -1cx-2 + 7x-1 + 2 Reorder the terms: a = 2 + -1bx-1 + -1cx-2 + -15x-2 + 7x-1
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