x(2x+1)=1830

Solution for x(2x+1)=1830 equation:

Simplifying
x(2x + 1) = 1830

Reorder the terms:
x(1 + 2x) = 1830
(1 * x + 2x * x) = 1830
(1x + 2x2) = 1830

Solving
1x + 2x2 = 1830

Solving for variable 'x'.

Reorder the terms:
-1830 + 1x + 2x2 = 1830 + -1830

Combine like terms: 1830 + -1830 = 0
-1830 + 1x + 2x2 = 0

Factor a trinomial.
(-61 + -2x)(30 + -1x) = 0

Subproblem 1
Set the factor '(-61 + -2x)' equal to zero and attempt to solve:

Simplifying
-61 + -2x = 0

Solving
-61 + -2x = 0

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

Add '61' to each side of the equation.
-61 + 61 + -2x = 0 + 61

Combine like terms: -61 + 61 = 0
0 + -2x = 0 + 61
-2x = 0 + 61

Combine like terms: 0 + 61 = 61
-2x = 61

Divide each side by '-2'.
x = -30.5

Simplifying
x = -30.5
Subproblem 2
Set the factor '(30 + -1x)' equal to zero and attempt to solve:

Simplifying
30 + -1x = 0

Solving
30 + -1x = 0

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

Add '-30' to each side of the equation.
30 + -30 + -1x = 0 + -30

Combine like terms: 30 + -30 = 0
0 + -1x = 0 + -30
-1x = 0 + -30

Combine like terms: 0 + -30 = -30
-1x = -30

Divide each side by '-1'.
x = 30

Simplifying
x = 30
Solution
x = {-30.5, 30}