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Simplifying (p + -2)(5p + 3) + (p + -2)(p + -2) = 0 Reorder the terms: (-2 + p)(5p + 3) + (p + -2)(p + -2) = 0 Reorder the terms: (-2 + p)(3 + 5p) + (p + -2)(p + -2) = 0 Multiply (-2 + p) * (3 + 5p) (-2(3 + 5p) + p(3 + 5p)) + (p + -2)(p + -2) = 0 ((3 * -2 + 5p * -2) + p(3 + 5p)) + (p + -2)(p + -2) = 0 ((-6 + -10p) + p(3 + 5p)) + (p + -2)(p + -2) = 0 (-6 + -10p + (3 * p + 5p * p)) + (p + -2)(p + -2) = 0 (-6 + -10p + (3p + 5p2)) + (p + -2)(p + -2) = 0 Combine like terms: -10p + 3p = -7p (-6 + -7p + 5p2) + (p + -2)(p + -2) = 0 Reorder the terms: -6 + -7p + 5p2 + (-2 + p)(p + -2) = 0 Reorder the terms: -6 + -7p + 5p2 + (-2 + p)(-2 + p) = 0 Multiply (-2 + p) * (-2 + p) -6 + -7p + 5p2 + (-2(-2 + p) + p(-2 + p)) = 0 -6 + -7p + 5p2 + ((-2 * -2 + p * -2) + p(-2 + p)) = 0 -6 + -7p + 5p2 + ((4 + -2p) + p(-2 + p)) = 0 -6 + -7p + 5p2 + (4 + -2p + (-2 * p + p * p)) = 0 -6 + -7p + 5p2 + (4 + -2p + (-2p + p2)) = 0 Combine like terms: -2p + -2p = -4p -6 + -7p + 5p2 + (4 + -4p + p2) = 0 Reorder the terms: -6 + 4 + -7p + -4p + 5p2 + p2 = 0 Combine like terms: -6 + 4 = -2 -2 + -7p + -4p + 5p2 + p2 = 0 Combine like terms: -7p + -4p = -11p -2 + -11p + 5p2 + p2 = 0 Combine like terms: 5p2 + p2 = 6p2 -2 + -11p + 6p2 = 0 Solving -2 + -11p + 6p2 = 0 Solving for variable 'p'. Factor a trinomial. (-1 + -6p)(2 + -1p) = 0Subproblem 1
Set the factor '(-1 + -6p)' equal to zero and attempt to solve: Simplifying -1 + -6p = 0 Solving -1 + -6p = 0 Move all terms containing p to the left, all other terms to the right. Add '1' to each side of the equation. -1 + 1 + -6p = 0 + 1 Combine like terms: -1 + 1 = 0 0 + -6p = 0 + 1 -6p = 0 + 1 Combine like terms: 0 + 1 = 1 -6p = 1 Divide each side by '-6'. p = -0.1666666667 Simplifying p = -0.1666666667Subproblem 2
Set the factor '(2 + -1p)' equal to zero and attempt to solve: Simplifying 2 + -1p = 0 Solving 2 + -1p = 0 Move all terms containing p to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + -1p = 0 + -2 Combine like terms: 2 + -2 = 0 0 + -1p = 0 + -2 -1p = 0 + -2 Combine like terms: 0 + -2 = -2 -1p = -2 Divide each side by '-1'. p = 2 Simplifying p = 2Solution
p = {-0.1666666667, 2}
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