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

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

Simplifying
x2 + (a + 1) * x + (3a + 1) = 0

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

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

Reorder the terms:
x2 + (ax + 1x) + (3a + 1) = 0
x2 + (ax + 1x) + (3a + 1) = 0

Reorder the terms:
x2 + ax + 1x + (1 + 3a) = 0

Remove parenthesis around (1 + 3a)
x2 + ax + 1x + 1 + 3a = 0

Reorder the terms:
1 + 3a + ax + 1x + x2 = 0

Solving
1 + 3a + ax + 1x + x2 = 0

Solving for variable 'a'.

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

Add '-1' to each side of the equation.
1 + 3a + ax + 1x + -1 + x2 = 0 + -1

Reorder the terms:
1 + -1 + 3a + ax + 1x + x2 = 0 + -1

Combine like terms: 1 + -1 = 0
0 + 3a + ax + 1x + x2 = 0 + -1
3a + ax + 1x + x2 = 0 + -1

Combine like terms: 0 + -1 = -1
3a + ax + 1x + x2 = -1

Add '-1x' to each side of the equation.
3a + ax + 1x + -1x + x2 = -1 + -1x

Combine like terms: 1x + -1x = 0
3a + ax + 0 + x2 = -1 + -1x
3a + ax + x2 = -1 + -1x

Add '-1x2' to each side of the equation.
3a + ax + x2 + -1x2 = -1 + -1x + -1x2

Combine like terms: x2 + -1x2 = 0
3a + ax + 0 = -1 + -1x + -1x2
3a + ax = -1 + -1x + -1x2

Reorder the terms:
1 + 3a + ax + x + x2 = -1 + -1x + -1x2 + 1 + x + x2

Reorder the terms:
1 + 3a + ax + x + x2 = -1 + 1 + -1x + x + -1x2 + x2

Combine like terms: -1 + 1 = 0
1 + 3a + ax + x + x2 = 0 + -1x + x + -1x2 + x2
1 + 3a + ax + x + x2 = -1x + x + -1x2 + x2

Combine like terms: -1x + x = 0
1 + 3a + ax + x + x2 = 0 + -1x2 + x2
1 + 3a + ax + x + x2 = -1x2 + x2

Combine like terms: -1x2 + x2 = 0
1 + 3a + ax + x + x2 = 0

The solution to this equation could not be determined.