p(2p+4)+4p(p-5)=

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Solution for p(2p+4)+4p(p-5)= equation: 


Simplifying
p(2p + 4) + 4p(p + -5) = 0

Reorder the terms:
p(4 + 2p) + 4p(p + -5) = 0
(4 * p + 2p * p) + 4p(p + -5) = 0
(4p + 2p2) + 4p(p + -5) = 0

Reorder the terms:
4p + 2p2 + 4p(-5 + p) = 0
4p + 2p2 + (-5 * 4p + p * 4p) = 0
4p + 2p2 + (-20p + 4p2) = 0

Reorder the terms:
4p + -20p + 2p2 + 4p2 = 0

Combine like terms: 4p + -20p = -16p
-16p + 2p2 + 4p2 = 0

Combine like terms: 2p2 + 4p2 = 6p2
-16p + 6p2 = 0

Solving
-16p + 6p2 = 0

Solving for variable 'p'.

Factor out the Greatest Common Factor (GCF), '2p'.
2p(-8 + 3p) = 0

Ignore the factor 2.

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 '(-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
Solution
p = {0, 2.666666667}

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