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

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


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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

Solving
2x + 2x2 = -4x + 4x2

Solving for variable 'x'.

Reorder the terms:
2x + 4x + 2x2 + -4x2 = -4x + 4x2 + 4x + -4x2

Combine like terms: 2x + 4x = 6x
6x + 2x2 + -4x2 = -4x + 4x2 + 4x + -4x2

Combine like terms: 2x2 + -4x2 = -2x2
6x + -2x2 = -4x + 4x2 + 4x + -4x2

Reorder the terms:
6x + -2x2 = -4x + 4x + 4x2 + -4x2

Combine like terms: -4x + 4x = 0
6x + -2x2 = 0 + 4x2 + -4x2
6x + -2x2 = 4x2 + -4x2

Combine like terms: 4x2 + -4x2 = 0
6x + -2x2 = 0

Factor out the Greatest Common Factor (GCF), '2x'.
2x(3 + -1x) = 0

Ignore the factor 2.

Subproblem 1
Set the factor 'x' equal to zero and attempt to solve:

Simplifying
x = 0

Solving
x = 0

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

Simplifying
x = 0

Subproblem 2
Set the factor '(3 + -1x)' equal to zero and attempt to solve:

Simplifying
3 + -1x = 0

Solving
3 + -1x = 0

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

Add '-3' to each side of the equation.
3 + -3 + -1x = 0 + -3

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

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

Divide each side by '-1'.
x = 3

Simplifying
x = 3
Solution
x = {0, 3}

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