x(2x+1)=18+x

Solution for x(2x+1)=18+x equation:

Simplifying
x(2x + 1) = 18 + x

Reorder the terms:
x(1 + 2x) = 18 + x
(1 * x + 2x * x) = 18 + x
(1x + 2x2) = 18 + x

Solving
1x + 2x2 = 18 + x

Solving for variable 'x'.

Reorder the terms:
-18 + 1x + -1x + 2x2 = 18 + x + -18 + -1x

Combine like terms: 1x + -1x = 0
-18 + 0 + 2x2 = 18 + x + -18 + -1x
-18 + 2x2 = 18 + x + -18 + -1x

Reorder the terms:
-18 + 2x2 = 18 + -18 + x + -1x

Combine like terms: 18 + -18 = 0
-18 + 2x2 = 0 + x + -1x
-18 + 2x2 = x + -1x

Combine like terms: x + -1x = 0
-18 + 2x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-9 + x2) = 0

Factor a difference between two squares.
2((3 + x)(-3 + x)) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(3 + x)' equal to zero and attempt to solve:

Simplifying
3 + x = 0

Solving
3 + x = 0

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

Add '-3' to each side of the equation.
3 + -3 + x = 0 + -3

Combine like terms: 3 + -3 = 0
0 + x = 0 + -3
x = 0 + -3

Combine like terms: 0 + -3 = -3
x = -3

Simplifying
x = -3
Subproblem 2
Set the factor '(-3 + x)' equal to zero and attempt to solve:

Simplifying
-3 + x = 0

Solving
-3 + x = 0

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

Add '3' to each side of the equation.
-3 + 3 + x = 0 + 3

Combine like terms: -3 + 3 = 0
0 + x = 0 + 3
x = 0 + 3

Combine like terms: 0 + 3 = 3
x = 3

Simplifying
x = 3
Solution
x = {-3, 3}