(x+3)(x+1)=6(x-4)

Solution for (x+3)(x+1)=6(x-4) equation:

Simplifying
(x + 3)(x + 1) = 6(x + -4)

Reorder the terms:
(3 + x)(x + 1) = 6(x + -4)

Reorder the terms:
(3 + x)(1 + x) = 6(x + -4)

Multiply (3 + x) * (1 + x)
(3(1 + x) + x(1 + x)) = 6(x + -4)
((1 * 3 + x * 3) + x(1 + x)) = 6(x + -4)
((3 + 3x) + x(1 + x)) = 6(x + -4)
(3 + 3x + (1 * x + x * x)) = 6(x + -4)
(3 + 3x + (1x + x2)) = 6(x + -4)

Combine like terms: 3x + 1x = 4x
(3 + 4x + x2) = 6(x + -4)

Reorder the terms:
3 + 4x + x2 = 6(-4 + x)
3 + 4x + x2 = (-4 * 6 + x * 6)
3 + 4x + x2 = (-24 + 6x)

Solving
3 + 4x + x2 = -24 + 6x

Solving for variable 'x'.

Reorder the terms:
3 + 24 + 4x + -6x + x2 = -24 + 6x + 24 + -6x

Combine like terms: 3 + 24 = 27
27 + 4x + -6x + x2 = -24 + 6x + 24 + -6x

Combine like terms: 4x + -6x = -2x
27 + -2x + x2 = -24 + 6x + 24 + -6x

Reorder the terms:
27 + -2x + x2 = -24 + 24 + 6x + -6x

Combine like terms: -24 + 24 = 0
27 + -2x + x2 = 0 + 6x + -6x
27 + -2x + x2 = 6x + -6x

Combine like terms: 6x + -6x = 0
27 + -2x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '-27' to each side of the equation.
27 + -2x + -27 + x2 = 0 + -27

Reorder the terms:
27 + -27 + -2x + x2 = 0 + -27

Combine like terms: 27 + -27 = 0
0 + -2x + x2 = 0 + -27
-2x + x2 = 0 + -27

Combine like terms: 0 + -27 = -27
-2x + x2 = -27

The x term is -2x.  Take half its coefficient (-1).
Square it (1) and add it to both sides.

Add '1' to each side of the equation.
-2x + 1 + x2 = -27 + 1

Reorder the terms:
1 + -2x + x2 = -27 + 1

Combine like terms: -27 + 1 = -26
1 + -2x + x2 = -26

Factor a perfect square on the left side:
(x + -1)(x + -1) = -26

Can't calculate square root of the right side.

The solution to this equation could not be determined.