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

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

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

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

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

Multiply (1 + x) * (1 + 2x)
(1(1 + 2x) + x(1 + 2x)) = 3
((1 * 1 + 2x * 1) + x(1 + 2x)) = 3
((1 + 2x) + x(1 + 2x)) = 3
(1 + 2x + (1 * x + 2x * x)) = 3
(1 + 2x + (1x + 2x2)) = 3

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

Solving
1 + 3x + 2x2 = 3

Solving for variable 'x'.

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

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

Combine like terms: 3 + -3 = 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}