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Simplifying (p2 + 4p + -23) + -1(3p2 + -23p + -23) = 0 Reorder the terms: (-23 + 4p + p2) + -1(3p2 + -23p + -23) = 0 Remove parenthesis around (-23 + 4p + p2) -23 + 4p + p2 + -1(3p2 + -23p + -23) = 0 Reorder the terms: -23 + 4p + p2 + -1(-23 + -23p + 3p2) = 0 -23 + 4p + p2 + (-23 * -1 + -23p * -1 + 3p2 * -1) = 0 -23 + 4p + p2 + (23 + 23p + -3p2) = 0 Reorder the terms: -23 + 23 + 4p + 23p + p2 + -3p2 = 0 Combine like terms: -23 + 23 = 0 0 + 4p + 23p + p2 + -3p2 = 0 4p + 23p + p2 + -3p2 = 0 Combine like terms: 4p + 23p = 27p 27p + p2 + -3p2 = 0 Combine like terms: p2 + -3p2 = -2p2 27p + -2p2 = 0 Solving 27p + -2p2 = 0 Solving for variable 'p'. Factor out the Greatest Common Factor (GCF), 'p'. p(27 + -2p) = 0Subproblem 1
Set the factor 'p' equal to zero and attempt to solve: Simplifying p = 0 Solving p = 0 Move all terms containing p to the left, all other terms to the right. Simplifying p = 0Subproblem 2
Set the factor '(27 + -2p)' equal to zero and attempt to solve: Simplifying 27 + -2p = 0 Solving 27 + -2p = 0 Move all terms containing p to the left, all other terms to the right. Add '-27' to each side of the equation. 27 + -27 + -2p = 0 + -27 Combine like terms: 27 + -27 = 0 0 + -2p = 0 + -27 -2p = 0 + -27 Combine like terms: 0 + -27 = -27 -2p = -27 Divide each side by '-2'. p = 13.5 Simplifying p = 13.5Solution
p = {0, 13.5}
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