2=x(2x+3)

Solution for 2=x(2x+3) equation:

Simplifying
2 = x(2x + 3)

Reorder the terms:
2 = x(3 + 2x)
2 = (3 * x + 2x * x)
2 = (3x + 2x2)

Solving
2 = 3x + 2x2

Solving for variable 'x'.

Reorder the terms:
2 + -3x + -2x2 = 3x + -3x + 2x2 + -2x2

Combine like terms: 3x + -3x = 0
2 + -3x + -2x2 = 0 + 2x2 + -2x2
2 + -3x + -2x2 = 2x2 + -2x2

Combine like terms: 2x2 + -2x2 = 0
2 + -3x + -2x2 = 0

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

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

Simplifying
1 + -2x = 0

Solving
1 + -2x = 0

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

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

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

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

Divide each side by '-2'.
x = 0.5

Simplifying
x = 0.5
Subproblem 2
Set the factor '(2 + x)' equal to zero and attempt to solve:

Simplifying
2 + x = 0

Solving
2 + x = 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 + x = 0 + -2

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

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

Simplifying
x = -2
Solution
x = {0.5, -2}