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Simplifying 15p2 + 24p = 12p + -5p2 Reorder the terms: 24p + 15p2 = 12p + -5p2 Solving 24p + 15p2 = 12p + -5p2 Solving for variable 'p'. Reorder the terms: 24p + -12p + 15p2 + 5p2 = 12p + -5p2 + -12p + 5p2 Combine like terms: 24p + -12p = 12p 12p + 15p2 + 5p2 = 12p + -5p2 + -12p + 5p2 Combine like terms: 15p2 + 5p2 = 20p2 12p + 20p2 = 12p + -5p2 + -12p + 5p2 Reorder the terms: 12p + 20p2 = 12p + -12p + -5p2 + 5p2 Combine like terms: 12p + -12p = 0 12p + 20p2 = 0 + -5p2 + 5p2 12p + 20p2 = -5p2 + 5p2 Combine like terms: -5p2 + 5p2 = 0 12p + 20p2 = 0 Factor out the Greatest Common Factor (GCF), '4p'. 4p(3 + 5p) = 0 Ignore the factor 4.Subproblem 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 '(3 + 5p)' equal to zero and attempt to solve: Simplifying 3 + 5p = 0 Solving 3 + 5p = 0 Move all terms containing p to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + 5p = 0 + -3 Combine like terms: 3 + -3 = 0 0 + 5p = 0 + -3 5p = 0 + -3 Combine like terms: 0 + -3 = -3 5p = -3 Divide each side by '5'. p = -0.6 Simplifying p = -0.6Solution
p = {0, -0.6}
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