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Simplifying p(p + -3) + -1p(p + 5) = 2(3p + 3) + -4(5p + -3) Reorder the terms: p(-3 + p) + -1p(p + 5) = 2(3p + 3) + -4(5p + -3) (-3 * p + p * p) + -1p(p + 5) = 2(3p + 3) + -4(5p + -3) (-3p + p2) + -1p(p + 5) = 2(3p + 3) + -4(5p + -3) Reorder the terms: -3p + p2 + -1p(5 + p) = 2(3p + 3) + -4(5p + -3) -3p + p2 + (5 * -1p + p * -1p) = 2(3p + 3) + -4(5p + -3) -3p + p2 + (-5p + -1p2) = 2(3p + 3) + -4(5p + -3) Reorder the terms: -3p + -5p + p2 + -1p2 = 2(3p + 3) + -4(5p + -3) Combine like terms: -3p + -5p = -8p -8p + p2 + -1p2 = 2(3p + 3) + -4(5p + -3) Combine like terms: p2 + -1p2 = 0 -8p + 0 = 2(3p + 3) + -4(5p + -3) -8p = 2(3p + 3) + -4(5p + -3) Reorder the terms: -8p = 2(3 + 3p) + -4(5p + -3) -8p = (3 * 2 + 3p * 2) + -4(5p + -3) -8p = (6 + 6p) + -4(5p + -3) Reorder the terms: -8p = 6 + 6p + -4(-3 + 5p) -8p = 6 + 6p + (-3 * -4 + 5p * -4) -8p = 6 + 6p + (12 + -20p) Reorder the terms: -8p = 6 + 12 + 6p + -20p Combine like terms: 6 + 12 = 18 -8p = 18 + 6p + -20p Combine like terms: 6p + -20p = -14p -8p = 18 + -14p Solving -8p = 18 + -14p Solving for variable 'p'. Move all terms containing p to the left, all other terms to the right. Add '14p' to each side of the equation. -8p + 14p = 18 + -14p + 14p Combine like terms: -8p + 14p = 6p 6p = 18 + -14p + 14p Combine like terms: -14p + 14p = 0 6p = 18 + 0 6p = 18 Divide each side by '6'. p = 3 Simplifying p = 3
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