x(2x+1)=10

Solution for x(2x+1)=10 equation:

Simplifying
x(2x + 1) = 10

Reorder the terms:
x(1 + 2x) = 10
(1 * x + 2x * x) = 10
(1x + 2x2) = 10

Solving
1x + 2x2 = 10

Solving for variable 'x'.

Reorder the terms:
-10 + 1x + 2x2 = 10 + -10

Combine like terms: 10 + -10 = 0
-10 + 1x + 2x2 = 0

Factor a trinomial.
(-5 + -2x)(2 + -1x) = 0

Subproblem 1
Set the factor '(-5 + -2x)' equal to zero and attempt to solve:

Simplifying
-5 + -2x = 0

Solving
-5 + -2x = 0

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

Add '5' to each side of the equation.
-5 + 5 + -2x = 0 + 5

Combine like terms: -5 + 5 = 0
0 + -2x = 0 + 5
-2x = 0 + 5

Combine like terms: 0 + 5 = 5
-2x = 5

Divide each side by '-2'.
x = -2.5

Simplifying
x = -2.5
Subproblem 2
Set the factor '(2 + -1x)' equal to zero and attempt to solve:

Simplifying
2 + -1x = 0

Solving
2 + -1x = 0

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

Add '-2' to each side of the equation.
2 + -2 + -1x = 0 + -2

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

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

Divide each side by '-1'.
x = 2

Simplifying
x = 2
Solution
x = {-2.5, 2}