(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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