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Simplifying 2x3 + 12x2 + -77x + -15 = (x + -4)(2x2 + px + 3) + r Reorder the terms: -15 + -77x + 12x2 + 2x3 = (x + -4)(2x2 + px + 3) + r Reorder the terms: -15 + -77x + 12x2 + 2x3 = (-4 + x)(2x2 + px + 3) + r Reorder the terms: -15 + -77x + 12x2 + 2x3 = (-4 + x)(3 + px + 2x2) + r Multiply (-4 + x) * (3 + px + 2x2) -15 + -77x + 12x2 + 2x3 = (-4(3 + px + 2x2) + x(3 + px + 2x2)) + r -15 + -77x + 12x2 + 2x3 = ((3 * -4 + px * -4 + 2x2 * -4) + x(3 + px + 2x2)) + r -15 + -77x + 12x2 + 2x3 = ((-12 + -4px + -8x2) + x(3 + px + 2x2)) + r -15 + -77x + 12x2 + 2x3 = (-12 + -4px + -8x2 + (3 * x + px * x + 2x2 * x)) + r Reorder the terms: -15 + -77x + 12x2 + 2x3 = (-12 + -4px + -8x2 + (px2 + 3x + 2x3)) + r -15 + -77x + 12x2 + 2x3 = (-12 + -4px + -8x2 + (px2 + 3x + 2x3)) + r Reorder the terms: -15 + -77x + 12x2 + 2x3 = (-12 + -4px + px2 + 3x + -8x2 + 2x3) + r -15 + -77x + 12x2 + 2x3 = (-12 + -4px + px2 + 3x + -8x2 + 2x3) + r Reorder the terms: -15 + -77x + 12x2 + 2x3 = -12 + -4px + px2 + r + 3x + -8x2 + 2x3 Add '-2x3' to each side of the equation. -15 + -77x + 12x2 + 2x3 + -2x3 = -12 + -4px + px2 + r + 3x + -8x2 + 2x3 + -2x3 Combine like terms: 2x3 + -2x3 = 0 -15 + -77x + 12x2 + 0 = -12 + -4px + px2 + r + 3x + -8x2 + 2x3 + -2x3 -15 + -77x + 12x2 = -12 + -4px + px2 + r + 3x + -8x2 + 2x3 + -2x3 Combine like terms: 2x3 + -2x3 = 0 -15 + -77x + 12x2 = -12 + -4px + px2 + r + 3x + -8x2 + 0 -15 + -77x + 12x2 = -12 + -4px + px2 + r + 3x + -8x2 Solving -15 + -77x + 12x2 = -12 + -4px + px2 + r + 3x + -8x2 Solving for variable 'x'. Reorder the terms: -15 + 12 + 4px + -1px2 + -1r + -77x + -3x + 12x2 + 8x2 = -12 + -4px + px2 + r + 3x + -8x2 + 12 + 4px + -1px2 + -1r + -3x + 8x2 Combine like terms: -15 + 12 = -3 -3 + 4px + -1px2 + -1r + -77x + -3x + 12x2 + 8x2 = -12 + -4px + px2 + r + 3x + -8x2 + 12 + 4px + -1px2 + -1r + -3x + 8x2 Combine like terms: -77x + -3x = -80x -3 + 4px + -1px2 + -1r + -80x + 12x2 + 8x2 = -12 + -4px + px2 + r + 3x + -8x2 + 12 + 4px + -1px2 + -1r + -3x + 8x2 Combine like terms: 12x2 + 8x2 = 20x2 -3 + 4px + -1px2 + -1r + -80x + 20x2 = -12 + -4px + px2 + r + 3x + -8x2 + 12 + 4px + -1px2 + -1r + -3x + 8x2 Reorder the terms: -3 + 4px + -1px2 + -1r + -80x + 20x2 = -12 + 12 + -4px + 4px + px2 + -1px2 + r + -1r + 3x + -3x + -8x2 + 8x2 Combine like terms: -12 + 12 = 0 -3 + 4px + -1px2 + -1r + -80x + 20x2 = 0 + -4px + 4px + px2 + -1px2 + r + -1r + 3x + -3x + -8x2 + 8x2 -3 + 4px + -1px2 + -1r + -80x + 20x2 = -4px + 4px + px2 + -1px2 + r + -1r + 3x + -3x + -8x2 + 8x2 Combine like terms: -4px + 4px = 0 -3 + 4px + -1px2 + -1r + -80x + 20x2 = 0 + px2 + -1px2 + r + -1r + 3x + -3x + -8x2 + 8x2 -3 + 4px + -1px2 + -1r + -80x + 20x2 = px2 + -1px2 + r + -1r + 3x + -3x + -8x2 + 8x2 Combine like terms: px2 + -1px2 = 0 -3 + 4px + -1px2 + -1r + -80x + 20x2 = 0 + r + -1r + 3x + -3x + -8x2 + 8x2 -3 + 4px + -1px2 + -1r + -80x + 20x2 = r + -1r + 3x + -3x + -8x2 + 8x2 Combine like terms: r + -1r = 0 -3 + 4px + -1px2 + -1r + -80x + 20x2 = 0 + 3x + -3x + -8x2 + 8x2 -3 + 4px + -1px2 + -1r + -80x + 20x2 = 3x + -3x + -8x2 + 8x2 Combine like terms: 3x + -3x = 0 -3 + 4px + -1px2 + -1r + -80x + 20x2 = 0 + -8x2 + 8x2 -3 + 4px + -1px2 + -1r + -80x + 20x2 = -8x2 + 8x2 Combine like terms: -8x2 + 8x2 = 0 -3 + 4px + -1px2 + -1r + -80x + 20x2 = 0 The solution to this equation could not be determined.
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