(2p-7)(3p+8)=

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Solution for (2p-7)(3p+8)= equation:


Simplifying
(2p + -7)(3p + 8) = 0

Reorder the terms:
(-7 + 2p)(3p + 8) = 0

Reorder the terms:
(-7 + 2p)(8 + 3p) = 0

Multiply (-7 + 2p) * (8 + 3p)
(-7(8 + 3p) + 2p * (8 + 3p)) = 0
((8 * -7 + 3p * -7) + 2p * (8 + 3p)) = 0
((-56 + -21p) + 2p * (8 + 3p)) = 0
(-56 + -21p + (8 * 2p + 3p * 2p)) = 0
(-56 + -21p + (16p + 6p2)) = 0

Combine like terms: -21p + 16p = -5p
(-56 + -5p + 6p2) = 0

Solving
-56 + -5p + 6p2 = 0

Solving for variable 'p'.

Factor a trinomial.
(-8 + -3p)(7 + -2p) = 0

Subproblem 1

Set the factor '(-8 + -3p)' equal to zero and attempt to solve: Simplifying -8 + -3p = 0 Solving -8 + -3p = 0 Move all terms containing p to the left, all other terms to the right. Add '8' to each side of the equation. -8 + 8 + -3p = 0 + 8 Combine like terms: -8 + 8 = 0 0 + -3p = 0 + 8 -3p = 0 + 8 Combine like terms: 0 + 8 = 8 -3p = 8 Divide each side by '-3'. p = -2.666666667 Simplifying p = -2.666666667

Subproblem 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 = 3.5

Solution

p = {-2.666666667, 3.5}

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