(2x+1)2=(x-1)2+3x(x+1)

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Solution for (2x+1)2=(x-1)2+3x(x+1) equation: 


Simplifying
(2x + 1) * 2 = (x + -1) * 2 + 3x(x + 1)

Reorder the terms:
(1 + 2x) * 2 = (x + -1) * 2 + 3x(x + 1)

Reorder the terms for easier multiplication:
2(1 + 2x) = (x + -1) * 2 + 3x(x + 1)
(1 * 2 + 2x * 2) = (x + -1) * 2 + 3x(x + 1)
(2 + 4x) = (x + -1) * 2 + 3x(x + 1)

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

Reorder the terms for easier multiplication:
2 + 4x = 2(-1 + x) + 3x(x + 1)
2 + 4x = (-1 * 2 + x * 2) + 3x(x + 1)
2 + 4x = (-2 + 2x) + 3x(x + 1)

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

Combine like terms: 2x + 3x = 5x
2 + 4x = -2 + 5x + 3x2

Solving
2 + 4x = -2 + 5x + 3x2

Solving for variable 'x'.

Reorder the terms:
2 + 2 + 4x + -5x + -3x2 = -2 + 5x + 3x2 + 2 + -5x + -3x2

Combine like terms: 2 + 2 = 4
4 + 4x + -5x + -3x2 = -2 + 5x + 3x2 + 2 + -5x + -3x2

Combine like terms: 4x + -5x = -1x
4 + -1x + -3x2 = -2 + 5x + 3x2 + 2 + -5x + -3x2

Reorder the terms:
4 + -1x + -3x2 = -2 + 2 + 5x + -5x + 3x2 + -3x2

Combine like terms: -2 + 2 = 0
4 + -1x + -3x2 = 0 + 5x + -5x + 3x2 + -3x2
4 + -1x + -3x2 = 5x + -5x + 3x2 + -3x2

Combine like terms: 5x + -5x = 0
4 + -1x + -3x2 = 0 + 3x2 + -3x2
4 + -1x + -3x2 = 3x2 + -3x2

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

Factor a trinomial.
(1 + -1x)(4 + 3x) = 0


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

Simplifying
1 + -1x = 0

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

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

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

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

Simplifying
x = 1

Subproblem 2
Set the factor '(4 + 3x)' equal to zero and attempt to solve:

Simplifying
4 + 3x = 0

Solving
4 + 3x = 0

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

Add '-4' to each side of the equation.
4 + -4 + 3x = 0 + -4

Combine like terms: 4 + -4 = 0
0 + 3x = 0 + -4
3x = 0 + -4

Combine like terms: 0 + -4 = -4
3x = -4

Divide each side by '3'.
x = -1.333333333

Simplifying
x = -1.333333333
Solution
x = {1, -1.333333333}

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