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Simplifying 6p2 + 102p + 420 = 0 Reorder the terms: 420 + 102p + 6p2 = 0 Solving 420 + 102p + 6p2 = 0 Solving for variable 'p'. Factor out the Greatest Common Factor (GCF), '6'. 6(70 + 17p + p2) = 0 Factor a trinomial. 6((10 + p)(7 + p)) = 0 Ignore the factor 6.Subproblem 1
Set the factor '(10 + p)' equal to zero and attempt to solve: Simplifying 10 + p = 0 Solving 10 + p = 0 Move all terms containing p to the left, all other terms to the right. Add '-10' to each side of the equation. 10 + -10 + p = 0 + -10 Combine like terms: 10 + -10 = 0 0 + p = 0 + -10 p = 0 + -10 Combine like terms: 0 + -10 = -10 p = -10 Simplifying p = -10Subproblem 2
Set the factor '(7 + p)' equal to zero and attempt to solve: Simplifying 7 + p = 0 Solving 7 + p = 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 + p = 0 + -7 Combine like terms: 7 + -7 = 0 0 + p = 0 + -7 p = 0 + -7 Combine like terms: 0 + -7 = -7 p = -7 Simplifying p = -7Solution
p = {-10, -7}
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