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

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


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

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

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

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

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

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

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

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

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

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

Remove parenthesis around (2 + 2x)
-1 + -2x = 2 + 2x + -1

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

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

Solving
-1 + -2x = 1 + 2x

Solving for variable 'x'.

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

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

Combine like terms: -2x + -2x = -4x
-1 + -4x = 1 + 2x + -2x

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

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

Combine like terms: -1 + 1 = 0
0 + -4x = 1 + 1
-4x = 1 + 1

Combine like terms: 1 + 1 = 2
-4x = 2

Divide each side by '-4'.
x = -0.5

Simplifying
x = -0.5

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