x^2-(2k+3)x+3k+1=0

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


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

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

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

Reorder the terms:
x2 + (-2kx + -3x) + 3k + 1 = 0
x2 + (-2kx + -3x) + 3k + 1 = 0

Reorder the terms:
1 + 3k + -2kx + -3x + x2 = 0

Solving
1 + 3k + -2kx + -3x + x2 = 0

Solving for variable 'k'.

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

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

Reorder the terms:
1 + -1 + 3k + -2kx + -3x + x2 = 0 + -1

Combine like terms: 1 + -1 = 0
0 + 3k + -2kx + -3x + x2 = 0 + -1
3k + -2kx + -3x + x2 = 0 + -1

Combine like terms: 0 + -1 = -1
3k + -2kx + -3x + x2 = -1

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

Combine like terms: -3x + 3x = 0
3k + -2kx + 0 + x2 = -1 + 3x
3k + -2kx + x2 = -1 + 3x

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

Combine like terms: x2 + -1x2 = 0
3k + -2kx + 0 = -1 + 3x + -1x2
3k + -2kx = -1 + 3x + -1x2

Reorder the terms:
1 + 3k + -2kx + -3x + x2 = -1 + 3x + -1x2 + 1 + -3x + x2

Reorder the terms:
1 + 3k + -2kx + -3x + x2 = -1 + 1 + 3x + -3x + -1x2 + x2

Combine like terms: -1 + 1 = 0
1 + 3k + -2kx + -3x + x2 = 0 + 3x + -3x + -1x2 + x2
1 + 3k + -2kx + -3x + x2 = 3x + -3x + -1x2 + x2

Combine like terms: 3x + -3x = 0
1 + 3k + -2kx + -3x + x2 = 0 + -1x2 + x2
1 + 3k + -2kx + -3x + x2 = -1x2 + x2

Combine like terms: -1x2 + x2 = 0
1 + 3k + -2kx + -3x + x2 = 0

The solution to this equation could not be determined.

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