x(2x+1)=210

Solution for x(2x+1)=210 equation:

Simplifying
x(2x + 1) = 210

Reorder the terms:
x(1 + 2x) = 210
(1 * x + 2x * x) = 210
(1x + 2x2) = 210

Solving
1x + 2x2 = 210

Solving for variable 'x'.

Reorder the terms:
-210 + 1x + 2x2 = 210 + -210

Combine like terms: 210 + -210 = 0
-210 + 1x + 2x2 = 0

Factor a trinomial.
(-21 + -2x)(10 + -1x) = 0

Subproblem 1
Set the factor '(-21 + -2x)' equal to zero and attempt to solve:

Simplifying
-21 + -2x = 0

Solving
-21 + -2x = 0

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

Add '21' to each side of the equation.
-21 + 21 + -2x = 0 + 21

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

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

Divide each side by '-2'.
x = -10.5

Simplifying
x = -10.5
Subproblem 2
Set the factor '(10 + -1x)' equal to zero and attempt to solve:

Simplifying
10 + -1x = 0

Solving
10 + -1x = 0

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

Add '-10' to each side of the equation.
10 + -10 + -1x = 0 + -10

Combine like terms: 10 + -10 = 0
0 + -1x = 0 + -10
-1x = 0 + -10

Combine like terms: 0 + -10 = -10
-1x = -10

Divide each side by '-1'.
x = 10

Simplifying
x = 10
Solution
x = {-10.5, 10}