(x+3)(x+4)+8=x

Solution for (x+3)(x+4)+8=x equation:

Simplifying
(x + 3)(x + 4) + 8 = x

Reorder the terms:
(3 + x)(x + 4) + 8 = x

Reorder the terms:
(3 + x)(4 + x) + 8 = x

Multiply (3 + x) * (4 + x)
(3(4 + x) + x(4 + x)) + 8 = x
((4 * 3 + x * 3) + x(4 + x)) + 8 = x
((12 + 3x) + x(4 + x)) + 8 = x
(12 + 3x + (4 * x + x * x)) + 8 = x
(12 + 3x + (4x + x2)) + 8 = x

Combine like terms: 3x + 4x = 7x
(12 + 7x + x2) + 8 = x

Reorder the terms:
12 + 8 + 7x + x2 = x

Combine like terms: 12 + 8 = 20
20 + 7x + x2 = x

Solving
20 + 7x + x2 = x

Solving for variable 'x'.

Reorder the terms:
20 + 7x + -1x + x2 = x + -1x

Combine like terms: 7x + -1x = 6x
20 + 6x + x2 = x + -1x

Combine like terms: x + -1x = 0
20 + 6x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '-20' to each side of the equation.
20 + 6x + -20 + x2 = 0 + -20

Reorder the terms:
20 + -20 + 6x + x2 = 0 + -20

Combine like terms: 20 + -20 = 0
0 + 6x + x2 = 0 + -20
6x + x2 = 0 + -20

Combine like terms: 0 + -20 = -20
6x + x2 = -20

The x term is 6x.  Take half its coefficient (3).
Square it (9) and add it to both sides.

Add '9' to each side of the equation.
6x + 9 + x2 = -20 + 9

Reorder the terms:
9 + 6x + x2 = -20 + 9

Combine like terms: -20 + 9 = -11
9 + 6x + x2 = -11

Factor a perfect square on the left side:
(x + 3)(x + 3) = -11

Can't calculate square root of the right side.

The solution to this equation could not be determined.