(2x+1)(x+3)-x^2=21

Solution for (2x+1)(x+3)-x^2=21 equation:

Simplifying
(2x + 1)(x + 3) + -1x2 = 21

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

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

Multiply (1 + 2x) * (3 + x)
(1(3 + x) + 2x * (3 + x)) + -1x2 = 21
((3 * 1 + x * 1) + 2x * (3 + x)) + -1x2 = 21
((3 + 1x) + 2x * (3 + x)) + -1x2 = 21
(3 + 1x + (3 * 2x + x * 2x)) + -1x2 = 21
(3 + 1x + (6x + 2x2)) + -1x2 = 21

Combine like terms: 1x + 6x = 7x
(3 + 7x + 2x2) + -1x2 = 21

Combine like terms: 2x2 + -1x2 = 1x2
3 + 7x + 1x2 = 21

Solving
3 + 7x + 1x2 = 21

Solving for variable 'x'.

Reorder the terms:
3 + -21 + 7x + 1x2 = 21 + -21

Combine like terms: 3 + -21 = -18
-18 + 7x + 1x2 = 21 + -21

Combine like terms: 21 + -21 = 0
-18 + 7x + 1x2 = 0

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

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

Simplifying
-9 + -1x = 0

Solving
-9 + -1x = 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 + -1x = 0 + 9

Combine like terms: -9 + 9 = 0
0 + -1x = 0 + 9
-1x = 0 + 9

Combine like terms: 0 + 9 = 9
-1x = 9

Divide each side by '-1'.
x = -9

Simplifying
x = -9
Subproblem 2
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
Solution
x = {-9, 2}