105=(x)(2x+1)

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

Simplifying
105 = (x)(2x + 1)

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

Solving
105 = 1x + 2x2

Solving for variable 'x'.

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

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

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

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

Subproblem 1
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
Subproblem 2
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
Solution
x = {7, -7.5}