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Simplifying (2p + -7)(2p + 10) = 0 Reorder the terms: (-7 + 2p)(2p + 10) = 0 Reorder the terms: (-7 + 2p)(10 + 2p) = 0 Multiply (-7 + 2p) * (10 + 2p) (-7(10 + 2p) + 2p * (10 + 2p)) = 0 ((10 * -7 + 2p * -7) + 2p * (10 + 2p)) = 0 ((-70 + -14p) + 2p * (10 + 2p)) = 0 (-70 + -14p + (10 * 2p + 2p * 2p)) = 0 (-70 + -14p + (20p + 4p2)) = 0 Combine like terms: -14p + 20p = 6p (-70 + 6p + 4p2) = 0 Solving -70 + 6p + 4p2 = 0 Solving for variable 'p'. Factor out the Greatest Common Factor (GCF), '2'. 2(-35 + 3p + 2p2) = 0 Factor a trinomial. 2((-5 + -1p)(7 + -2p)) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-5 + -1p)' equal to zero and attempt to solve: Simplifying -5 + -1p = 0 Solving -5 + -1p = 0 Move all terms containing p to the left, all other terms to the right. Add '5' to each side of the equation. -5 + 5 + -1p = 0 + 5 Combine like terms: -5 + 5 = 0 0 + -1p = 0 + 5 -1p = 0 + 5 Combine like terms: 0 + 5 = 5 -1p = 5 Divide each side by '-1'. p = -5 Simplifying p = -5Subproblem 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 = {-5, 3.5}
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