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

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


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

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

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

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

Combine like terms: 1x + 1x = 2x
(1 + 2x + x2) + 3(x + 4) = x(x + -1) + 1

Reorder the terms:
1 + 2x + x2 + 3(4 + x) = x(x + -1) + 1
1 + 2x + x2 + (4 * 3 + x * 3) = x(x + -1) + 1
1 + 2x + x2 + (12 + 3x) = x(x + -1) + 1

Reorder the terms:
1 + 12 + 2x + 3x + x2 = x(x + -1) + 1

Combine like terms: 1 + 12 = 13
13 + 2x + 3x + x2 = x(x + -1) + 1

Combine like terms: 2x + 3x = 5x
13 + 5x + x2 = x(x + -1) + 1

Reorder the terms:
13 + 5x + x2 = x(-1 + x) + 1
13 + 5x + x2 = (-1 * x + x * x) + 1
13 + 5x + x2 = (-1x + x2) + 1

Reorder the terms:
13 + 5x + x2 = 1 + -1x + x2

Add '-1x2' to each side of the equation.
13 + 5x + x2 + -1x2 = 1 + -1x + x2 + -1x2

Combine like terms: x2 + -1x2 = 0
13 + 5x + 0 = 1 + -1x + x2 + -1x2
13 + 5x = 1 + -1x + x2 + -1x2

Combine like terms: x2 + -1x2 = 0
13 + 5x = 1 + -1x + 0
13 + 5x = 1 + -1x

Solving
13 + 5x = 1 + -1x

Solving for variable 'x'.

Move all terms containing x to the left, all other terms to the right.

Add 'x' to each side of the equation.
13 + 5x + x = 1 + -1x + x

Combine like terms: 5x + x = 6x
13 + 6x = 1 + -1x + x

Combine like terms: -1x + x = 0
13 + 6x = 1 + 0
13 + 6x = 1

Add '-13' to each side of the equation.
13 + -13 + 6x = 1 + -13

Combine like terms: 13 + -13 = 0
0 + 6x = 1 + -13
6x = 1 + -13

Combine like terms: 1 + -13 = -12
6x = -12

Divide each side by '6'.
x = -2

Simplifying
x = -2

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