3x+6=2x^2+4x

Solution for 3x+6=2x^2+4x equation:

Simplifying
3x + 6 = 2x2 + 4x

Reorder the terms:
6 + 3x = 2x2 + 4x

Reorder the terms:
6 + 3x = 4x + 2x2

Solving
6 + 3x = 4x + 2x2

Solving for variable 'x'.

Combine like terms: 3x + -4x = -1x
6 + -1x + -2x2 = 4x + 2x2 + -4x + -2x2

Reorder the terms:
6 + -1x + -2x2 = 4x + -4x + 2x2 + -2x2

Combine like terms: 4x + -4x = 0
6 + -1x + -2x2 = 0 + 2x2 + -2x2
6 + -1x + -2x2 = 2x2 + -2x2

Combine like terms: 2x2 + -2x2 = 0
6 + -1x + -2x2 = 0

Factor a trinomial.
(3 + -2x)(2 + x) = 0

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

Simplifying
3 + -2x = 0

Solving
3 + -2x = 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 + -2x = 0 + -3

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

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

Divide each side by '-2'.
x = 1.5

Simplifying
x = 1.5
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 = {1.5, -2}