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Simplifying 25p2 + -24p = 8p + 4p2 + -12 Reorder the terms: -24p + 25p2 = 8p + 4p2 + -12 Reorder the terms: -24p + 25p2 = -12 + 8p + 4p2 Solving -24p + 25p2 = -12 + 8p + 4p2 Solving for variable 'p'. Reorder the terms: 12 + -24p + -8p + 25p2 + -4p2 = -12 + 8p + 4p2 + 12 + -8p + -4p2 Combine like terms: -24p + -8p = -32p 12 + -32p + 25p2 + -4p2 = -12 + 8p + 4p2 + 12 + -8p + -4p2 Combine like terms: 25p2 + -4p2 = 21p2 12 + -32p + 21p2 = -12 + 8p + 4p2 + 12 + -8p + -4p2 Reorder the terms: 12 + -32p + 21p2 = -12 + 12 + 8p + -8p + 4p2 + -4p2 Combine like terms: -12 + 12 = 0 12 + -32p + 21p2 = 0 + 8p + -8p + 4p2 + -4p2 12 + -32p + 21p2 = 8p + -8p + 4p2 + -4p2 Combine like terms: 8p + -8p = 0 12 + -32p + 21p2 = 0 + 4p2 + -4p2 12 + -32p + 21p2 = 4p2 + -4p2 Combine like terms: 4p2 + -4p2 = 0 12 + -32p + 21p2 = 0 Factor a trinomial. (2 + -3p)(6 + -7p) = 0Subproblem 1
Set the factor '(2 + -3p)' equal to zero and attempt to solve: Simplifying 2 + -3p = 0 Solving 2 + -3p = 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 + -3p = 0 + -2 Combine like terms: 2 + -2 = 0 0 + -3p = 0 + -2 -3p = 0 + -2 Combine like terms: 0 + -2 = -2 -3p = -2 Divide each side by '-3'. p = 0.6666666667 Simplifying p = 0.6666666667Subproblem 2
Set the factor '(6 + -7p)' equal to zero and attempt to solve: Simplifying 6 + -7p = 0 Solving 6 + -7p = 0 Move all terms containing p to the left, all other terms to the right. Add '-6' to each side of the equation. 6 + -6 + -7p = 0 + -6 Combine like terms: 6 + -6 = 0 0 + -7p = 0 + -6 -7p = 0 + -6 Combine like terms: 0 + -6 = -6 -7p = -6 Divide each side by '-7'. p = 0.8571428571 Simplifying p = 0.8571428571Solution
p = {0.6666666667, 0.8571428571}
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