(x+1)(2x+1)=21

Solution for (x+1)(2x+1)=21 equation:

Simplifying
(x + 1)(2x + 1) = 21

Reorder the terms:
(1 + x)(2x + 1) = 21

Reorder the terms:
(1 + x)(1 + 2x) = 21

Multiply (1 + x) * (1 + 2x)
(1(1 + 2x) + x(1 + 2x)) = 21
((1 * 1 + 2x * 1) + x(1 + 2x)) = 21
((1 + 2x) + x(1 + 2x)) = 21
(1 + 2x + (1 * x + 2x * x)) = 21
(1 + 2x + (1x + 2x2)) = 21

Combine like terms: 2x + 1x = 3x
(1 + 3x + 2x2) = 21

Solving
1 + 3x + 2x2 = 21

Solving for variable 'x'.

Reorder the terms:
1 + -21 + 3x + 2x2 = 21 + -21

Combine like terms: 1 + -21 = -20
-20 + 3x + 2x2 = 21 + -21

Combine like terms: 21 + -21 = 0
-20 + 3x + 2x2 = 0

Factor a trinomial.
(-4 + -1x)(5 + -2x) = 0

Subproblem 1
Set the factor '(-4 + -1x)' equal to zero and attempt to solve:

Simplifying
-4 + -1x = 0

Solving
-4 + -1x = 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 + -1x = 0 + 4

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

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

Divide each side by '-1'.
x = -4

Simplifying
x = -4
Subproblem 2
Set the factor '(5 + -2x)' equal to zero and attempt to solve:

Simplifying
5 + -2x = 0

Solving
5 + -2x = 0

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

Add '-5' to each side of the equation.
5 + -5 + -2x = 0 + -5

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

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

Divide each side by '-2'.
x = 2.5

Simplifying
x = 2.5
Solution
x = {-4, 2.5}