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Simplifying (3p + 2)(5p + -7) = 0 Reorder the terms: (2 + 3p)(5p + -7) = 0 Reorder the terms: (2 + 3p)(-7 + 5p) = 0 Multiply (2 + 3p) * (-7 + 5p) (2(-7 + 5p) + 3p * (-7 + 5p)) = 0 ((-7 * 2 + 5p * 2) + 3p * (-7 + 5p)) = 0 ((-14 + 10p) + 3p * (-7 + 5p)) = 0 (-14 + 10p + (-7 * 3p + 5p * 3p)) = 0 (-14 + 10p + (-21p + 15p2)) = 0 Combine like terms: 10p + -21p = -11p (-14 + -11p + 15p2) = 0 Solving -14 + -11p + 15p2 = 0 Solving for variable 'p'. Factor a trinomial. (-2 + -3p)(7 + -5p) = 0Subproblem 1
Set the factor '(-2 + -3p)' equal to zero and attempt to solve: Simplifying -2 + -3p = 0 Solving -2 + -3p = 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 + -3p = 0 + 2 Combine like terms: -2 + 2 = 0 0 + -3p = 0 + 2 -3p = 0 + 2 Combine like terms: 0 + 2 = 2 -3p = 2 Divide each side by '-3'. p = -0.6666666667 Simplifying p = -0.6666666667Subproblem 2
Set the factor '(7 + -5p)' equal to zero and attempt to solve: Simplifying 7 + -5p = 0 Solving 7 + -5p = 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 + -5p = 0 + -7 Combine like terms: 7 + -7 = 0 0 + -5p = 0 + -7 -5p = 0 + -7 Combine like terms: 0 + -7 = -7 -5p = -7 Divide each side by '-5'. p = 1.4 Simplifying p = 1.4Solution
p = {-0.6666666667, 1.4}
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