x(x+1)+(x+2)+(x+3)+(x+4)=

Solution for x(x+1)+(x+2)+(x+3)+(x+4)= equation:

Simplifying
x(x + 1) + (x + 2) + (x + 3) + (x + 4) = 0

Reorder the terms:
x(1 + x) + (x + 2) + (x + 3) + (x + 4) = 0
(1 * x + x * x) + (x + 2) + (x + 3) + (x + 4) = 0
(1x + x2) + (x + 2) + (x + 3) + (x + 4) = 0

Reorder the terms:
1x + x2 + (2 + x) + (x + 3) + (x + 4) = 0

Remove parenthesis around (2 + x)
1x + x2 + 2 + x + (x + 3) + (x + 4) = 0

Reorder the terms:
1x + x2 + 2 + x + (3 + x) + (x + 4) = 0

Remove parenthesis around (3 + x)
1x + x2 + 2 + x + 3 + x + (x + 4) = 0

Reorder the terms:
1x + x2 + 2 + x + 3 + x + (4 + x) = 0

Remove parenthesis around (4 + x)
1x + x2 + 2 + x + 3 + x + 4 + x = 0

Reorder the terms:
2 + 3 + 4 + 1x + x + x + x + x2 = 0

Combine like terms: 2 + 3 = 5
5 + 4 + 1x + x + x + x + x2 = 0

Combine like terms: 5 + 4 = 9
9 + 1x + x + x + x + x2 = 0

Combine like terms: 1x + x = 2x
9 + 2x + x + x + x2 = 0

Combine like terms: 2x + x = 3x
9 + 3x + x + x2 = 0

Combine like terms: 3x + x = 4x
9 + 4x + x2 = 0

Solving
9 + 4x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '-9' to each side of the equation.
9 + 4x + -9 + x2 = 0 + -9

Reorder the terms:
9 + -9 + 4x + x2 = 0 + -9

Combine like terms: 9 + -9 = 0
0 + 4x + x2 = 0 + -9
4x + x2 = 0 + -9

Combine like terms: 0 + -9 = -9
4x + x2 = -9

The x term is 4x.  Take half its coefficient (2).
Square it (4) and add it to both sides.

Add '4' to each side of the equation.
4x + 4 + x2 = -9 + 4

Reorder the terms:
4 + 4x + x2 = -9 + 4

Combine like terms: -9 + 4 = -5
4 + 4x + x2 = -5

Factor a perfect square on the left side:
(x + 2)(x + 2) = -5

Can't calculate square root of the right side.

The solution to this equation could not be determined.