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Simplifying 0 = 6y2(p + r) + -2y(p + r) + 3(p + r) 0 = (p * 6y2 + r * 6y2) + -2y(p + r) + 3(p + r) 0 = (6py2 + 6ry2) + -2y(p + r) + 3(p + r) 0 = 6py2 + 6ry2 + (p * -2y + r * -2y) + 3(p + r) 0 = 6py2 + 6ry2 + (-2py + -2ry) + 3(p + r) 0 = 6py2 + 6ry2 + -2py + -2ry + (p * 3 + r * 3) 0 = 6py2 + 6ry2 + -2py + -2ry + (3p + 3r) Reorder the terms: 0 = 3p + -2py + 6py2 + 3r + -2ry + 6ry2 Solving 0 = 3p + -2py + 6py2 + 3r + -2ry + 6ry2 Solving for variable 'p'. Move all terms containing p to the left, all other terms to the right. Add '-3p' to each side of the equation. 0 + -3p = 3p + -2py + 6py2 + 3r + -2ry + -3p + 6ry2 Remove the zero: -3p = 3p + -2py + 6py2 + 3r + -2ry + -3p + 6ry2 Reorder the terms: -3p = 3p + -3p + -2py + 6py2 + 3r + -2ry + 6ry2 Combine like terms: 3p + -3p = 0 -3p = 0 + -2py + 6py2 + 3r + -2ry + 6ry2 -3p = -2py + 6py2 + 3r + -2ry + 6ry2 Add '2py' to each side of the equation. -3p + 2py = -2py + 6py2 + 3r + -2ry + 2py + 6ry2 Reorder the terms: -3p + 2py = -2py + 2py + 6py2 + 3r + -2ry + 6ry2 Combine like terms: -2py + 2py = 0 -3p + 2py = 0 + 6py2 + 3r + -2ry + 6ry2 -3p + 2py = 6py2 + 3r + -2ry + 6ry2 Add '-6py2' to each side of the equation. -3p + 2py + -6py2 = 6py2 + 3r + -2ry + -6py2 + 6ry2 Reorder the terms: -3p + 2py + -6py2 = 6py2 + -6py2 + 3r + -2ry + 6ry2 Combine like terms: 6py2 + -6py2 = 0 -3p + 2py + -6py2 = 0 + 3r + -2ry + 6ry2 -3p + 2py + -6py2 = 3r + -2ry + 6ry2 Reorder the terms: -3p + 2py + -6py2 + -3r + 2ry + -6ry2 = 3r + -3r + -2ry + 2ry + 6ry2 + -6ry2 Combine like terms: 3r + -3r = 0 -3p + 2py + -6py2 + -3r + 2ry + -6ry2 = 0 + -2ry + 2ry + 6ry2 + -6ry2 -3p + 2py + -6py2 + -3r + 2ry + -6ry2 = -2ry + 2ry + 6ry2 + -6ry2 Combine like terms: -2ry + 2ry = 0 -3p + 2py + -6py2 + -3r + 2ry + -6ry2 = 0 + 6ry2 + -6ry2 -3p + 2py + -6py2 + -3r + 2ry + -6ry2 = 6ry2 + -6ry2 Combine like terms: 6ry2 + -6ry2 = 0 -3p + 2py + -6py2 + -3r + 2ry + -6ry2 = 0 The solution to this equation could not be determined.
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