9p(2p+4)-3p(4p-15)=

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Solution for 9p(2p+4)-3p(4p-15)= equation: 


Simplifying
9p(2p + 4) + -3p(4p + -15) = 0

Reorder the terms:
9p(4 + 2p) + -3p(4p + -15) = 0
(4 * 9p + 2p * 9p) + -3p(4p + -15) = 0
(36p + 18p2) + -3p(4p + -15) = 0

Reorder the terms:
36p + 18p2 + -3p(-15 + 4p) = 0
36p + 18p2 + (-15 * -3p + 4p * -3p) = 0
36p + 18p2 + (45p + -12p2) = 0

Reorder the terms:
36p + 45p + 18p2 + -12p2 = 0

Combine like terms: 36p + 45p = 81p
81p + 18p2 + -12p2 = 0

Combine like terms: 18p2 + -12p2 = 6p2
81p + 6p2 = 0

Solving
81p + 6p2 = 0

Solving for variable 'p'.

Factor out the Greatest Common Factor (GCF), '3p'.
3p(27 + 2p) = 0

Ignore the factor 3.

Subproblem 1
Set the factor 'p' equal to zero and attempt to solve:

Simplifying
p = 0

Solving
p = 0

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

Simplifying
p = 0

Subproblem 2
Set the factor '(27 + 2p)' equal to zero and attempt to solve:

Simplifying
27 + 2p = 0

Solving
27 + 2p = 0

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

Add '-27' to each side of the equation.
27 + -27 + 2p = 0 + -27

Combine like terms: 27 + -27 = 0
0 + 2p = 0 + -27
2p = 0 + -27

Combine like terms: 0 + -27 = -27
2p = -27

Divide each side by '2'.
p = -13.5

Simplifying
p = -13.5
Solution
p = {0, -13.5}

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