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

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


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

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

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

Multiply (-7 + 3p) * (8 + 2p)
(-7(8 + 2p) + 3p * (8 + 2p)) = 0
((8 * -7 + 2p * -7) + 3p * (8 + 2p)) = 0
((-56 + -14p) + 3p * (8 + 2p)) = 0
(-56 + -14p + (8 * 3p + 2p * 3p)) = 0
(-56 + -14p + (24p + 6p2)) = 0

Combine like terms: -14p + 24p = 10p
(-56 + 10p + 6p2) = 0

Solving
-56 + 10p + 6p2 = 0

Solving for variable 'p'.

Factor out the Greatest Common Factor (GCF), '2'.
2(-28 + 5p + 3p2) = 0

Factor a trinomial.
2((-4 + -1p)(7 + -3p)) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(-4 + -1p)' equal to zero and attempt to solve:

Simplifying
-4 + -1p = 0

Solving
-4 + -1p = 0

Move all terms containing p to the left, all other terms to the right.

Add '4' to each side of the equation.
-4 + 4 + -1p = 0 + 4

Combine like terms: -4 + 4 = 0
0 + -1p = 0 + 4
-1p = 0 + 4

Combine like terms: 0 + 4 = 4
-1p = 4

Divide each side by '-1'.
p = -4

Simplifying
p = -4

Subproblem 2
Set the factor '(7 + -3p)' equal to zero and attempt to solve:

Simplifying
7 + -3p = 0

Solving
7 + -3p = 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 + -3p = 0 + -7

Combine like terms: 7 + -7 = 0
0 + -3p = 0 + -7
-3p = 0 + -7

Combine like terms: 0 + -7 = -7
-3p = -7

Divide each side by '-3'.
p = 2.333333333

Simplifying
p = 2.333333333
Solution
p = {-4, 2.333333333}

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