0.8p(4p+5)=4(0.5p-2)

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Solution for 0.8p(4p+5)=4(0.5p-2) equation: 


Simplifying
0.8p(4p + 5) = 4(0.5p + -2)

Reorder the terms:
0.8p(5 + 4p) = 4(0.5p + -2)
(5 * 0.8p + 4p * 0.8p) = 4(0.5p + -2)
(4p + 3.2p2) = 4(0.5p + -2)

Reorder the terms:
4p + 3.2p2 = 4(-2 + 0.5p)
4p + 3.2p2 = (-2 * 4 + 0.5p * 4)
4p + 3.2p2 = (-8 + 2p)

Solving
4p + 3.2p2 = -8 + 2p

Solving for variable 'p'.

Reorder the terms:
8 + 4p + -2p + 3.2p2 = -8 + 2p + 8 + -2p

Combine like terms: 4p + -2p = 2p
8 + 2p + 3.2p2 = -8 + 2p + 8 + -2p

Reorder the terms:
8 + 2p + 3.2p2 = -8 + 8 + 2p + -2p

Combine like terms: -8 + 8 = 0
8 + 2p + 3.2p2 = 0 + 2p + -2p
8 + 2p + 3.2p2 = 2p + -2p

Combine like terms: 2p + -2p = 0
8 + 2p + 3.2p2 = 0

Begin completing the square.  Divide all terms by
3.2 the coefficient of the squared term: 

Divide each side by '3.2'.
2.5 + 0.625p + p2 = 0

Move the constant term to the right:

Add '-2.5' to each side of the equation.
2.5 + 0.625p + -2.5 + p2 = 0 + -2.5

Reorder the terms:
2.5 + -2.5 + 0.625p + p2 = 0 + -2.5

Combine like terms: 2.5 + -2.5 = 0.0
0.0 + 0.625p + p2 = 0 + -2.5
0.625p + p2 = 0 + -2.5

Combine like terms: 0 + -2.5 = -2.5
0.625p + p2 = -2.5

The p term is 0.625p.  Take half its coefficient (0.3125).
Square it (0.09765625) and add it to both sides.

Add '0.09765625' to each side of the equation.
0.625p + 0.09765625 + p2 = -2.5 + 0.09765625

Reorder the terms:
0.09765625 + 0.625p + p2 = -2.5 + 0.09765625

Combine like terms: -2.5 + 0.09765625 = -2.40234375
0.09765625 + 0.625p + p2 = -2.40234375

Factor a perfect square on the left side:
(p + 0.3125)(p + 0.3125) = -2.40234375

Can't calculate square root of the right side.

The solution to this equation could not be determined.

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