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

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


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

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

Reorder the terms for easier multiplication:
2(1 + 2x) = x(2x + 1)
(1 * 2 + 2x * 2) = x(2x + 1)
(2 + 4x) = x(2x + 1)

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

Solving
2 + 4x = 1x + 2x2

Solving for variable 'x'.

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

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

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

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

Factor a trinomial.
(2 + -1x)(1 + 2x) = 0


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

Simplifying
2 + -1x = 0

Solving
2 + -1x = 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 + -1x = 0 + -2

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

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

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

Simplifying
x = 2

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

Simplifying
1 + 2x = 0

Solving
1 + 2x = 0

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

Add '-1' to each side of the equation.
1 + -1 + 2x = 0 + -1

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

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

Divide each side by '2'.
x = -0.5

Simplifying
x = -0.5
Solution
x = {2, -0.5}

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