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Simplifying 14p + -4p(2p + 3) = 0 Reorder the terms: 14p + -4p(3 + 2p) = 0 14p + (3 * -4p + 2p * -4p) = 0 14p + (-12p + -8p2) = 0 Combine like terms: 14p + -12p = 2p 2p + -8p2 = 0 Solving 2p + -8p2 = 0 Solving for variable 'p'. Factor out the Greatest Common Factor (GCF), '2p'. 2p(1 + -4p) = 0 Ignore the factor 2.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 '(1 + -4p)' equal to zero and attempt to solve: Simplifying 1 + -4p = 0 Solving 1 + -4p = 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 + -4p = 0 + -1 Combine like terms: 1 + -1 = 0 0 + -4p = 0 + -1 -4p = 0 + -1 Combine like terms: 0 + -1 = -1 -4p = -1 Divide each side by '-4'. p = 0.25 Simplifying p = 0.25Solution
p = {0, 0.25}
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