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

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


Simplifying
(3x2) + (p + 2) * x + 2p + 1 = 0

Reorder the terms:
(3x2) + (2 + p) * x + 2p + 1 = 0

Reorder the terms for easier multiplication:
(3x2) + x(2 + p) + 2p + 1 = 0
(3x2) + (2 * x + p * x) + 2p + 1 = 0

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

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

Solving
1 + 2p + px + 2x + (3x2) = 0

Solving for variable 'p'.

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

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

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

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

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

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

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

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

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

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

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

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

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

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

The solution to this equation could not be determined.

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