2(x^2)+1=(2x+1)(2x+1)

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


Simplifying
2(x2) + 1 = (2x + 1)(2x + 1)

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

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

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

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

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

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

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

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

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

Solving
2x2 = 4x + 4x2

Solving for variable 'x'.

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

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

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

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

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

Factor out the Greatest Common Factor (GCF), '-2x'.
-2x(2 + x) = 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 '(2 + x)' equal to zero and attempt to solve:

Simplifying
2 + x = 0

Solving
2 + x = 0

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

Add '-2' to each side of the equation.
2 + -2 + x = 0 + -2

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

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

Simplifying
x = -2
Solution
x = {0, -2}

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