(3x+1)2=19+(x-1)(x+1)

Solution for (3x+1)2=19+(x-1)(x+1) equation:

Simplifying
(3x + 1) * 2 = 19 + (x + -1)(x + 1)

Reorder the terms:
(1 + 3x) * 2 = 19 + (x + -1)(x + 1)

Reorder the terms for easier multiplication:
2(1 + 3x) = 19 + (x + -1)(x + 1)
(1 * 2 + 3x * 2) = 19 + (x + -1)(x + 1)
(2 + 6x) = 19 + (x + -1)(x + 1)

Reorder the terms:
2 + 6x = 19 + (-1 + x)(x + 1)

Reorder the terms:
2 + 6x = 19 + (-1 + x)(1 + x)

Multiply (-1 + x) * (1 + x)
2 + 6x = 19 + (-1(1 + x) + x(1 + x))
2 + 6x = 19 + ((1 * -1 + x * -1) + x(1 + x))
2 + 6x = 19 + ((-1 + -1x) + x(1 + x))
2 + 6x = 19 + (-1 + -1x + (1 * x + x * x))
2 + 6x = 19 + (-1 + -1x + (1x + x2))

Combine like terms: -1x + 1x = 0
2 + 6x = 19 + (-1 + 0 + x2)
2 + 6x = 19 + (-1 + x2)

Combine like terms: 19 + -1 = 18
2 + 6x = 18 + x2

Solving
2 + 6x = 18 + x2

Solving for variable 'x'.

Reorder the terms:
2 + -18 + 6x + -1x2 = 18 + x2 + -18 + -1x2

Combine like terms: 2 + -18 = -16
-16 + 6x + -1x2 = 18 + x2 + -18 + -1x2

Reorder the terms:
-16 + 6x + -1x2 = 18 + -18 + x2 + -1x2

Combine like terms: 18 + -18 = 0
-16 + 6x + -1x2 = 0 + x2 + -1x2
-16 + 6x + -1x2 = x2 + -1x2

Combine like terms: x2 + -1x2 = 0
-16 + 6x + -1x2 = 0

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

Divide each side by '-1'.
16 + -6x + x2 = 0

Move the constant term to the right:

Add '-16' to each side of the equation.
16 + -6x + -16 + x2 = 0 + -16

Reorder the terms:
16 + -16 + -6x + x2 = 0 + -16

Combine like terms: 16 + -16 = 0
0 + -6x + x2 = 0 + -16
-6x + x2 = 0 + -16

Combine like terms: 0 + -16 = -16
-6x + x2 = -16

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 = -16 + 9

Reorder the terms:
9 + -6x + x2 = -16 + 9

Combine like terms: -16 + 9 = -7
9 + -6x + x2 = -7

Factor a perfect square on the left side:
(x + -3)(x + -3) = -7

Can't calculate square root of the right side.

The solution to this equation could not be determined.