p(2p+1)-3p=4p-6

Solution for p(2p+1)-3p=4p-6 equation:

Simplifying
p(2p + 1) + -3p = 4p + -6

Reorder the terms:
p(1 + 2p) + -3p = 4p + -6
(1 * p + 2p * p) + -3p = 4p + -6
(1p + 2p2) + -3p = 4p + -6

Reorder the terms:
1p + -3p + 2p2 = 4p + -6

Combine like terms: 1p + -3p = -2p
-2p + 2p2 = 4p + -6

Reorder the terms:
-2p + 2p2 = -6 + 4p

Solving
-2p + 2p2 = -6 + 4p

Solving for variable 'p'.

Reorder the terms:
6 + -2p + -4p + 2p2 = -6 + 4p + 6 + -4p

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

Reorder the terms:
6 + -6p + 2p2 = -6 + 6 + 4p + -4p

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

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

Factor out the Greatest Common Factor (GCF), '2'.
2(3 + -3p + p2) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(3 + -3p + p2)' equal to zero and attempt to solve:

Simplifying
3 + -3p + p2 = 0

Solving
3 + -3p + p2 = 0

Begin completing the square.

Move the constant term to the right:

Add '-3' to each side of the equation.
3 + -3p + -3 + p2 = 0 + -3

Reorder the terms:
3 + -3 + -3p + p2 = 0 + -3

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

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

The p term is -3p.  Take half its coefficient (-1.5).
Square it (2.25) and add it to both sides.

Add '2.25' to each side of the equation.
-3p + 2.25 + p2 = -3 + 2.25

Reorder the terms:
2.25 + -3p + p2 = -3 + 2.25

Combine like terms: -3 + 2.25 = -0.75
2.25 + -3p + p2 = -0.75

Factor a perfect square on the left side:
(p + -1.5)(p + -1.5) = -0.75

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.