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

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


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

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

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

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

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

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

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

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

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

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

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

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

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

Solving
-1 + 3x + 5x2 = 1

Solving for variable 'x'.

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

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

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

Factor a trinomial.
(-1 + -1x)(2 + -5x) = 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 '(2 + -5x)' equal to zero and attempt to solve:

Simplifying
2 + -5x = 0

Solving
2 + -5x = 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 + -5x = 0 + -2

Combine like terms: 2 + -2 = 0
0 + -5x = 0 + -2
-5x = 0 + -2

Combine like terms: 0 + -2 = -2
-5x = -2

Divide each side by '-5'.
x = 0.4

Simplifying
x = 0.4
Solution
x = {-1, 0.4}

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