(2x+1)(x+1)-(2x+1)(2+x)=0

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Solution for (2x+1)(x+1)-(2x+1)(2+x)=0 equation:


Simplifying
(2x + 1)(x + 1) + -1(2x + 1)(2 + x) = 0

Reorder the terms:
(1 + 2x)(x + 1) + -1(2x + 1)(2 + x) = 0

Reorder the terms:
(1 + 2x)(1 + x) + -1(2x + 1)(2 + x) = 0

Multiply (1 + 2x) * (1 + x)
(1(1 + x) + 2x * (1 + x)) + -1(2x + 1)(2 + x) = 0
((1 * 1 + x * 1) + 2x * (1 + x)) + -1(2x + 1)(2 + x) = 0
((1 + 1x) + 2x * (1 + x)) + -1(2x + 1)(2 + x) = 0
(1 + 1x + (1 * 2x + x * 2x)) + -1(2x + 1)(2 + x) = 0
(1 + 1x + (2x + 2x2)) + -1(2x + 1)(2 + x) = 0

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

Reorder the terms:
1 + 3x + 2x2 + -1(1 + 2x)(2 + x) = 0

Multiply (1 + 2x) * (2 + x)
1 + 3x + 2x2 + -1(1(2 + x) + 2x * (2 + x)) = 0
1 + 3x + 2x2 + -1((2 * 1 + x * 1) + 2x * (2 + x)) = 0
1 + 3x + 2x2 + -1((2 + 1x) + 2x * (2 + x)) = 0
1 + 3x + 2x2 + -1(2 + 1x + (2 * 2x + x * 2x)) = 0
1 + 3x + 2x2 + -1(2 + 1x + (4x + 2x2)) = 0

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

Reorder the terms:
1 + -2 + 3x + -5x + 2x2 + -2x2 = 0

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

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

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

Solving
-1 + -2x = 0

Solving for variable 'x'.

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

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