21=x(1+2x)

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

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

Solving
21 = 1x + 2x2

Solving for variable 'x'.

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

Combine like terms: 1x + -1x = 0
21 + -1x + -2x2 = 0 + 2x2 + -2x2
21 + -1x + -2x2 = 2x2 + -2x2

Combine like terms: 2x2 + -2x2 = 0
21 + -1x + -2x2 = 0

Factor a trinomial.
(3 + -1x)(7 + 2x) = 0

Subproblem 1
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
Subproblem 2
Set the factor '(7 + 2x)' equal to zero and attempt to solve:

Simplifying
7 + 2x = 0

Solving
7 + 2x = 0

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

Add '-7' to each side of the equation.
7 + -7 + 2x = 0 + -7

Combine like terms: 7 + -7 = 0
0 + 2x = 0 + -7
2x = 0 + -7

Combine like terms: 0 + -7 = -7
2x = -7

Divide each side by '2'.
x = -3.5

Simplifying
x = -3.5
Solution
x = {3, -3.5}