p(2p-1)+(4+p)3=

Solution for p(2p-1)+(4+p)3= equation:

Simplifying
p(2p + -1) + (4 + p) * 3 = 0

Reorder the terms:
p(-1 + 2p) + (4 + p) * 3 = 0
(-1 * p + 2p * p) + (4 + p) * 3 = 0
(-1p + 2p2) + (4 + p) * 3 = 0

Reorder the terms for easier multiplication:
-1p + 2p2 + 3(4 + p) = 0
-1p + 2p2 + (4 * 3 + p * 3) = 0
-1p + 2p2 + (12 + 3p) = 0

Reorder the terms:
12 + -1p + 3p + 2p2 = 0

Combine like terms: -1p + 3p = 2p
12 + 2p + 2p2 = 0

Solving
12 + 2p + 2p2 = 0

Solving for variable 'p'.

Factor out the Greatest Common Factor (GCF), '2'.
2(6 + p + p2) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(6 + p + p2)' equal to zero and attempt to solve:

Simplifying
6 + p + p2 = 0

Solving
6 + p + p2 = 0

Begin completing the square.

Move the constant term to the right:

Add '-6' to each side of the equation.
6 + p + -6 + p2 = 0 + -6

Reorder the terms:
6 + -6 + p + p2 = 0 + -6

Combine like terms: 6 + -6 = 0
0 + p + p2 = 0 + -6
p + p2 = 0 + -6

Combine like terms: 0 + -6 = -6
p + p2 = -6

The p term is p.  Take half its coefficient (0.5).
Square it (0.25) and add it to both sides.

Add '0.25' to each side of the equation.
p + 0.25 + p2 = -6 + 0.25

Reorder the terms:
0.25 + p + p2 = -6 + 0.25

Combine like terms: -6 + 0.25 = -5.75
0.25 + p + p2 = -5.75

Factor a perfect square on the left side:
(p + 0.5)(p + 0.5) = -5.75

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.