(x+4)(x+1)=-16

Solution for (x+4)(x+1)=-16 equation:

Simplifying
(x + 4)(x + 1) = -16

Reorder the terms:
(4 + x)(x + 1) = -16

Reorder the terms:
(4 + x)(1 + x) = -16

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

Combine like terms: 4x + 1x = 5x
(4 + 5x + x2) = -16

Solving
4 + 5x + x2 = -16

Solving for variable 'x'.

Reorder the terms:
4 + 16 + 5x + x2 = -16 + 16

Combine like terms: 4 + 16 = 20
20 + 5x + x2 = -16 + 16

Combine like terms: -16 + 16 = 0
20 + 5x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '-20' to each side of the equation.
20 + 5x + -20 + x2 = 0 + -20

Reorder the terms:
20 + -20 + 5x + x2 = 0 + -20

Combine like terms: 20 + -20 = 0
0 + 5x + x2 = 0 + -20
5x + x2 = 0 + -20

Combine like terms: 0 + -20 = -20
5x + x2 = -20

The x term is 5x.  Take half its coefficient (2.5).
Square it (6.25) and add it to both sides.

Add '6.25' to each side of the equation.
5x + 6.25 + x2 = -20 + 6.25

Reorder the terms:
6.25 + 5x + x2 = -20 + 6.25

Combine like terms: -20 + 6.25 = -13.75
6.25 + 5x + x2 = -13.75

Factor a perfect square on the left side:
(x + 2.5)(x + 2.5) = -13.75

Can't calculate square root of the right side.

The solution to this equation could not be determined.