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

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


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

Reorder the terms:
0 = 3p(2 + p) + -2(p + -4)
0 = (2 * 3p + p * 3p) + -2(p + -4)
0 = (6p + 3p2) + -2(p + -4)

Reorder the terms:
0 = 6p + 3p2 + -2(-4 + p)
0 = 6p + 3p2 + (-4 * -2 + p * -2)
0 = 6p + 3p2 + (8 + -2p)

Reorder the terms:
0 = 8 + 6p + -2p + 3p2

Combine like terms: 6p + -2p = 4p
0 = 8 + 4p + 3p2

Solving
0 = 8 + 4p + 3p2

Solving for variable 'p'.

Combine like terms: 0 + -8 = -8
-8 + -4p + -3p2 = 8 + 4p + 3p2 + -8 + -4p + -3p2

Reorder the terms:
-8 + -4p + -3p2 = 8 + -8 + 4p + -4p + 3p2 + -3p2

Combine like terms: 8 + -8 = 0
-8 + -4p + -3p2 = 0 + 4p + -4p + 3p2 + -3p2
-8 + -4p + -3p2 = 4p + -4p + 3p2 + -3p2

Combine like terms: 4p + -4p = 0
-8 + -4p + -3p2 = 0 + 3p2 + -3p2
-8 + -4p + -3p2 = 3p2 + -3p2

Combine like terms: 3p2 + -3p2 = 0
-8 + -4p + -3p2 = 0

Factor out the Greatest Common Factor (GCF), '-1'.
-1(8 + 4p + 3p2) = 0

Ignore the factor -1.

Subproblem 1
Set the factor '(8 + 4p + 3p2)' equal to zero and attempt to solve:

Simplifying
8 + 4p + 3p2 = 0

Solving
8 + 4p + 3p2 = 0

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

Divide each side by '3'.
2.666666667 + 1.333333333p + p2 = 0

Move the constant term to the right:

Add '-2.666666667' to each side of the equation.
2.666666667 + 1.333333333p + -2.666666667 + p2 = 0 + -2.666666667

Reorder the terms:
2.666666667 + -2.666666667 + 1.333333333p + p2 = 0 + -2.666666667

Combine like terms: 2.666666667 + -2.666666667 = 0.000000000
0.000000000 + 1.333333333p + p2 = 0 + -2.666666667
1.333333333p + p2 = 0 + -2.666666667

Combine like terms: 0 + -2.666666667 = -2.666666667
1.333333333p + p2 = -2.666666667

The p term is 1.333333333p.  Take half its coefficient (0.6666666665).
Square it (0.4444444442) and add it to both sides.

Add '0.4444444442' to each side of the equation.
1.333333333p + 0.4444444442 + p2 = -2.666666667 + 0.4444444442

Reorder the terms:
0.4444444442 + 1.333333333p + p2 = -2.666666667 + 0.4444444442

Combine like terms: -2.666666667 + 0.4444444442 = -2.2222222228
0.4444444442 + 1.333333333p + p2 = -2.2222222228

Factor a perfect square on the left side:
(p + 0.6666666665)(p + 0.6666666665) = -2.2222222228

Can't calculate square root of the right side.

The solution to this equation could not be determined.

This subproblem is being ignored because a solution could not be determined.

The solution to this equation could not be determined.

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