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Simplifying 3p(2p + -1) + -9 = 6(p + 1) * 2 Reorder the terms: 3p(-1 + 2p) + -9 = 6(p + 1) * 2 (-1 * 3p + 2p * 3p) + -9 = 6(p + 1) * 2 (-3p + 6p2) + -9 = 6(p + 1) * 2 Reorder the terms: -9 + -3p + 6p2 = 6(p + 1) * 2 Reorder the terms: -9 + -3p + 6p2 = 6(1 + p) * 2 Reorder the terms for easier multiplication: -9 + -3p + 6p2 = 6 * 2(1 + p) Multiply 6 * 2 -9 + -3p + 6p2 = 12(1 + p) -9 + -3p + 6p2 = (1 * 12 + p * 12) -9 + -3p + 6p2 = (12 + 12p) Solving -9 + -3p + 6p2 = 12 + 12p Solving for variable 'p'. Reorder the terms: -9 + -12 + -3p + -12p + 6p2 = 12 + 12p + -12 + -12p Combine like terms: -9 + -12 = -21 -21 + -3p + -12p + 6p2 = 12 + 12p + -12 + -12p Combine like terms: -3p + -12p = -15p -21 + -15p + 6p2 = 12 + 12p + -12 + -12p Reorder the terms: -21 + -15p + 6p2 = 12 + -12 + 12p + -12p Combine like terms: 12 + -12 = 0 -21 + -15p + 6p2 = 0 + 12p + -12p -21 + -15p + 6p2 = 12p + -12p Combine like terms: 12p + -12p = 0 -21 + -15p + 6p2 = 0 Factor out the Greatest Common Factor (GCF), '3'. 3(-7 + -5p + 2p2) = 0 Factor a trinomial. 3((-1 + -1p)(7 + -2p)) = 0 Ignore the factor 3.Subproblem 1
Set the factor '(-1 + -1p)' equal to zero and attempt to solve: Simplifying -1 + -1p = 0 Solving -1 + -1p = 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 + -1p = 0 + 1 Combine like terms: -1 + 1 = 0 0 + -1p = 0 + 1 -1p = 0 + 1 Combine like terms: 0 + 1 = 1 -1p = 1 Divide each side by '-1'. p = -1 Simplifying p = -1Subproblem 2
Set the factor '(7 + -2p)' equal to zero and attempt to solve: Simplifying 7 + -2p = 0 Solving 7 + -2p = 0 Move all terms containing p to the left, all other terms to the right. Add '-7' to each side of the equation. 7 + -7 + -2p = 0 + -7 Combine like terms: 7 + -7 = 0 0 + -2p = 0 + -7 -2p = 0 + -7 Combine like terms: 0 + -7 = -7 -2p = -7 Divide each side by '-2'. p = 3.5 Simplifying p = 3.5Solution
p = {-1, 3.5}
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