(x+1)2+3(x-4)=x(x-1)+1

Solution for (x+1)2+3(x-4)=x(x-1)+1 equation:

Simplifying
(x + 1) * 2 + 3(x + -4) = x(x + -1) + 1

Reorder the terms:
(1 + x) * 2 + 3(x + -4) = x(x + -1) + 1

Reorder the terms for easier multiplication:
2(1 + x) + 3(x + -4) = x(x + -1) + 1
(1 * 2 + x * 2) + 3(x + -4) = x(x + -1) + 1
(2 + 2x) + 3(x + -4) = x(x + -1) + 1

Reorder the terms:
2 + 2x + 3(-4 + x) = x(x + -1) + 1
2 + 2x + (-4 * 3 + x * 3) = x(x + -1) + 1
2 + 2x + (-12 + 3x) = x(x + -1) + 1

Reorder the terms:
2 + -12 + 2x + 3x = x(x + -1) + 1

Combine like terms: 2 + -12 = -10
-10 + 2x + 3x = x(x + -1) + 1

Combine like terms: 2x + 3x = 5x
-10 + 5x = x(x + -1) + 1

Reorder the terms:
-10 + 5x = x(-1 + x) + 1
-10 + 5x = (-1 * x + x * x) + 1
-10 + 5x = (-1x + x2) + 1

Reorder the terms:
-10 + 5x = 1 + -1x + x2

Solving
-10 + 5x = 1 + -1x + x2

Solving for variable 'x'.

Reorder the terms:
-10 + -1 + 5x + x + -1x2 = 1 + -1x + x2 + -1 + x + -1x2

Combine like terms: -10 + -1 = -11
-11 + 5x + x + -1x2 = 1 + -1x + x2 + -1 + x + -1x2

Combine like terms: 5x + x = 6x
-11 + 6x + -1x2 = 1 + -1x + x2 + -1 + x + -1x2

Reorder the terms:
-11 + 6x + -1x2 = 1 + -1 + -1x + x + x2 + -1x2

Combine like terms: 1 + -1 = 0
-11 + 6x + -1x2 = 0 + -1x + x + x2 + -1x2
-11 + 6x + -1x2 = -1x + x + x2 + -1x2

Combine like terms: -1x + x = 0
-11 + 6x + -1x2 = 0 + x2 + -1x2
-11 + 6x + -1x2 = x2 + -1x2

Combine like terms: x2 + -1x2 = 0
-11 + 6x + -1x2 = 0

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

Divide each side by '-1'.
11 + -6x + x2 = 0

Move the constant term to the right:

Add '-11' to each side of the equation.
11 + -6x + -11 + x2 = 0 + -11

Reorder the terms:
11 + -11 + -6x + x2 = 0 + -11

Combine like terms: 11 + -11 = 0
0 + -6x + x2 = 0 + -11
-6x + x2 = 0 + -11

Combine like terms: 0 + -11 = -11
-6x + x2 = -11

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 = -11 + 9

Reorder the terms:
9 + -6x + x2 = -11 + 9

Combine like terms: -11 + 9 = -2
9 + -6x + x2 = -2

Factor a perfect square on the left side:
(x + -3)(x + -3) = -2

Can't calculate square root of the right side.

The solution to this equation could not be determined.