(x+1)(2x+1)=28

Solution for (x+1)(2x+1)=28 equation:

Simplifying
(x + 1)(2x + 1) = 28

Reorder the terms:
(1 + x)(2x + 1) = 28

Reorder the terms:
(1 + x)(1 + 2x) = 28

Multiply (1 + x) * (1 + 2x)
(1(1 + 2x) + x(1 + 2x)) = 28
((1 * 1 + 2x * 1) + x(1 + 2x)) = 28
((1 + 2x) + x(1 + 2x)) = 28
(1 + 2x + (1 * x + 2x * x)) = 28
(1 + 2x + (1x + 2x2)) = 28

Combine like terms: 2x + 1x = 3x
(1 + 3x + 2x2) = 28

Solving
1 + 3x + 2x2 = 28

Solving for variable 'x'.

Reorder the terms:
1 + -28 + 3x + 2x2 = 28 + -28

Combine like terms: 1 + -28 = -27
-27 + 3x + 2x2 = 28 + -28

Combine like terms: 28 + -28 = 0
-27 + 3x + 2x2 = 0

Factor a trinomial.
(-9 + -2x)(3 + -1x) = 0

Subproblem 1
Set the factor '(-9 + -2x)' equal to zero and attempt to solve:

Simplifying
-9 + -2x = 0

Solving
-9 + -2x = 0

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

Add '9' to each side of the equation.
-9 + 9 + -2x = 0 + 9

Combine like terms: -9 + 9 = 0
0 + -2x = 0 + 9
-2x = 0 + 9

Combine like terms: 0 + 9 = 9
-2x = 9

Divide each side by '-2'.
x = -4.5

Simplifying
x = -4.5
Subproblem 2
Set the factor '(3 + -1x)' equal to zero and attempt to solve:

Simplifying
3 + -1x = 0

Solving
3 + -1x = 0

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

Add '-3' to each side of the equation.
3 + -3 + -1x = 0 + -3

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

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

Divide each side by '-1'.
x = 3

Simplifying
x = 3
Solution
x = {-4.5, 3}