x*(2x+1)=105

Solution for x*(2x+1)=105 equation:

Simplifying
x(2x + 1) = 105

Reorder the terms:
x(1 + 2x) = 105
(1 * x + 2x * x) = 105
(1x + 2x2) = 105

Solving
1x + 2x2 = 105

Solving for variable 'x'.

Reorder the terms:
-105 + 1x + 2x2 = 105 + -105

Combine like terms: 105 + -105 = 0
-105 + 1x + 2x2 = 0

Factor a trinomial.
(-15 + -2x)(7 + -1x) = 0

Subproblem 1
Set the factor '(-15 + -2x)' equal to zero and attempt to solve:

Simplifying
-15 + -2x = 0

Solving
-15 + -2x = 0

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

Add '15' to each side of the equation.
-15 + 15 + -2x = 0 + 15

Combine like terms: -15 + 15 = 0
0 + -2x = 0 + 15
-2x = 0 + 15

Combine like terms: 0 + 15 = 15
-2x = 15

Divide each side by '-2'.
x = -7.5

Simplifying
x = -7.5
Subproblem 2
Set the factor '(7 + -1x)' equal to zero and attempt to solve:

Simplifying
7 + -1x = 0

Solving
7 + -1x = 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 + -1x = 0 + -7

Combine like terms: 7 + -7 = 0
0 + -1x = 0 + -7
-1x = 0 + -7

Combine like terms: 0 + -7 = -7
-1x = -7

Divide each side by '-1'.
x = 7

Simplifying
x = 7
Solution
x = {-7.5, 7}