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

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


Simplifying
(x + 1)(x + -1) + (x + 2)(x + 2) = (2x + 1)(x + 1)

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

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

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

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

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

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

Multiply (2 + x) * (2 + x)
-1 + x2 + (2(2 + x) + x(2 + x)) = (2x + 1)(x + 1)
-1 + x2 + ((2 * 2 + x * 2) + x(2 + x)) = (2x + 1)(x + 1)
-1 + x2 + ((4 + 2x) + x(2 + x)) = (2x + 1)(x + 1)
-1 + x2 + (4 + 2x + (2 * x + x * x)) = (2x + 1)(x + 1)
-1 + x2 + (4 + 2x + (2x + x2)) = (2x + 1)(x + 1)

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

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

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

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

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

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

Multiply (1 + 2x) * (1 + x)
3 + 4x + 2x2 = (1(1 + x) + 2x * (1 + x))
3 + 4x + 2x2 = ((1 * 1 + x * 1) + 2x * (1 + x))
3 + 4x + 2x2 = ((1 + 1x) + 2x * (1 + x))
3 + 4x + 2x2 = (1 + 1x + (1 * 2x + x * 2x))
3 + 4x + 2x2 = (1 + 1x + (2x + 2x2))

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

Add '-2x2' to each side of the equation.
3 + 4x + 2x2 + -2x2 = 1 + 3x + 2x2 + -2x2

Combine like terms: 2x2 + -2x2 = 0
3 + 4x + 0 = 1 + 3x + 2x2 + -2x2
3 + 4x = 1 + 3x + 2x2 + -2x2

Combine like terms: 2x2 + -2x2 = 0
3 + 4x = 1 + 3x + 0
3 + 4x = 1 + 3x

Solving
3 + 4x = 1 + 3x

Solving for variable 'x'.

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

Add '-3x' to each side of the equation.
3 + 4x + -3x = 1 + 3x + -3x

Combine like terms: 4x + -3x = 1x
3 + 1x = 1 + 3x + -3x

Combine like terms: 3x + -3x = 0
3 + 1x = 1 + 0
3 + 1x = 1

Add '-3' to each side of the equation.
3 + -3 + 1x = 1 + -3

Combine like terms: 3 + -3 = 0
0 + 1x = 1 + -3
1x = 1 + -3

Combine like terms: 1 + -3 = -2
1x = -2

Divide each side by '1'.
x = -2

Simplifying
x = -2

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