(x+1)-(x+4)(x-4)=19

Solution for (x+1)-(x+4)(x-4)=19 equation:

Simplifying
(x + 1) + -1(x + 4)(x + -4) = 19

Reorder the terms:
(1 + x) + -1(x + 4)(x + -4) = 19

Remove parenthesis around (1 + x)
1 + x + -1(x + 4)(x + -4) = 19

Reorder the terms:
1 + x + -1(4 + x)(x + -4) = 19

Reorder the terms:
1 + x + -1(4 + x)(-4 + x) = 19

Multiply (4 + x) * (-4 + x)
1 + x + -1(4(-4 + x) + x(-4 + x)) = 19
1 + x + -1((-4 * 4 + x * 4) + x(-4 + x)) = 19
1 + x + -1((-16 + 4x) + x(-4 + x)) = 19
1 + x + -1(-16 + 4x + (-4 * x + x * x)) = 19
1 + x + -1(-16 + 4x + (-4x + x2)) = 19

Combine like terms: 4x + -4x = 0
1 + x + -1(-16 + 0 + x2) = 19
1 + x + -1(-16 + x2) = 19
1 + x + (-16 * -1 + x2 * -1) = 19
1 + x + (16 + -1x2) = 19

Reorder the terms:
1 + 16 + x + -1x2 = 19

Combine like terms: 1 + 16 = 17
17 + x + -1x2 = 19

Solving
17 + x + -1x2 = 19

Solving for variable 'x'.

Reorder the terms:
17 + -19 + x + -1x2 = 19 + -19

Combine like terms: 17 + -19 = -2
-2 + x + -1x2 = 19 + -19

Combine like terms: 19 + -19 = 0
-2 + x + -1x2 = 0

Begin completing the square.  Divide all terms by
-1 the coefficient of the squared term: 

Divide each side by '-1'.
2 + -1x + x2 = 0

Move the constant term to the right:

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

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

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

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

The x term is x.  Take half its coefficient (0.5).
Square it (0.25) and add it to both sides.

Add '0.25' to each side of the equation.
-1x + 0.25 + x2 = -2 + 0.25

Reorder the terms:
0.25 + -1x + x2 = -2 + 0.25

Combine like terms: -2 + 0.25 = -1.75
0.25 + -1x + x2 = -1.75

Factor a perfect square on the left side:
(x + 0.5)(x + 0.5) = -1.75

Can't calculate square root of the right side.

The solution to this equation could not be determined.