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Simplifying (7p + -3)(4p + 8) = 0 Reorder the terms: (-3 + 7p)(4p + 8) = 0 Reorder the terms: (-3 + 7p)(8 + 4p) = 0 Multiply (-3 + 7p) * (8 + 4p) (-3(8 + 4p) + 7p * (8 + 4p)) = 0 ((8 * -3 + 4p * -3) + 7p * (8 + 4p)) = 0 ((-24 + -12p) + 7p * (8 + 4p)) = 0 (-24 + -12p + (8 * 7p + 4p * 7p)) = 0 (-24 + -12p + (56p + 28p2)) = 0 Combine like terms: -12p + 56p = 44p (-24 + 44p + 28p2) = 0 Solving -24 + 44p + 28p2 = 0 Solving for variable 'p'. Factor out the Greatest Common Factor (GCF), '4'. 4(-6 + 11p + 7p2) = 0 Factor a trinomial. 4((-2 + -1p)(3 + -7p)) = 0 Ignore the factor 4.Subproblem 1
Set the factor '(-2 + -1p)' equal to zero and attempt to solve: Simplifying -2 + -1p = 0 Solving -2 + -1p = 0 Move all terms containing p to the left, all other terms to the right. Add '2' to each side of the equation. -2 + 2 + -1p = 0 + 2 Combine like terms: -2 + 2 = 0 0 + -1p = 0 + 2 -1p = 0 + 2 Combine like terms: 0 + 2 = 2 -1p = 2 Divide each side by '-1'. p = -2 Simplifying p = -2Subproblem 2
Set the factor '(3 + -7p)' equal to zero and attempt to solve: Simplifying 3 + -7p = 0 Solving 3 + -7p = 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 + -7p = 0 + -3 Combine like terms: 3 + -3 = 0 0 + -7p = 0 + -3 -7p = 0 + -3 Combine like terms: 0 + -3 = -3 -7p = -3 Divide each side by '-7'. p = 0.4285714286 Simplifying p = 0.4285714286Solution
p = {-2, 0.4285714286}
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