px^2-p(p+3)x+2p(p+1)=0

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Solution for px^2-p(p+3)x+2p(p+1)=0 equation: 


Simplifying
px2 + -1p(p + 3) * x + 2p(p + 1) = 0

Reorder the terms:
px2 + -1p(3 + p) * x + 2p(p + 1) = 0

Reorder the terms for easier multiplication:
px2 + -1p * x(3 + p) + 2p(p + 1) = 0

Multiply p * x
px2 + -1px(3 + p) + 2p(p + 1) = 0
px2 + (3 * -1px + p * -1px) + 2p(p + 1) = 0
px2 + (-3px + -1p2x) + 2p(p + 1) = 0

Reorder the terms:
px2 + -3px + -1p2x + 2p(1 + p) = 0
px2 + -3px + -1p2x + (1 * 2p + p * 2p) = 0
px2 + -3px + -1p2x + (2p + 2p2) = 0

Reorder the terms:
2p + -3px + px2 + 2p2 + -1p2x = 0

Solving
2p + -3px + px2 + 2p2 + -1p2x = 0

Solving for variable 'p'.

Factor out the Greatest Common Factor (GCF), 'p'.
p(2 + -3x + x2 + 2p + -1px) = 0


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 '(2 + -3x + x2 + 2p + -1px)' equal to zero and attempt to solve:

Simplifying
2 + -3x + x2 + 2p + -1px = 0

Reorder the terms:
2 + 2p + -1px + -3x + x2 = 0

Solving
2 + 2p + -1px + -3x + x2 = 0

Move all terms containing p to the left, all other terms to the right.

Add '-2' to each side of the equation.
2 + 2p + -1px + -3x + -2 + x2 = 0 + -2

Reorder the terms:
2 + -2 + 2p + -1px + -3x + x2 = 0 + -2

Combine like terms: 2 + -2 = 0
0 + 2p + -1px + -3x + x2 = 0 + -2
2p + -1px + -3x + x2 = 0 + -2

Combine like terms: 0 + -2 = -2
2p + -1px + -3x + x2 = -2

Add '3x' to each side of the equation.
2p + -1px + -3x + 3x + x2 = -2 + 3x

Combine like terms: -3x + 3x = 0
2p + -1px + 0 + x2 = -2 + 3x
2p + -1px + x2 = -2 + 3x

Add '-1x2' to each side of the equation.
2p + -1px + x2 + -1x2 = -2 + 3x + -1x2

Combine like terms: x2 + -1x2 = 0
2p + -1px + 0 = -2 + 3x + -1x2
2p + -1px = -2 + 3x + -1x2

The solution to this equation could not be determined.

This subproblem is being ignored because a solution could not be determined.
Solution
p = {0}

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