2x^2+4x=x^2-x-6

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

Simplifying
2x2 + 4x = x2 + -1x + -6

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

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

Solving
4x + 2x2 = -6 + -1x + x2

Solving for variable 'x'.

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

Combine like terms: 4x + x = 5x
6 + 5x + 2x2 + -1x2 = -6 + -1x + x2 + 6 + x + -1x2

Combine like terms: 2x2 + -1x2 = 1x2
6 + 5x + 1x2 = -6 + -1x + x2 + 6 + x + -1x2

Reorder the terms:
6 + 5x + 1x2 = -6 + 6 + -1x + x + x2 + -1x2

Combine like terms: -6 + 6 = 0
6 + 5x + 1x2 = 0 + -1x + x + x2 + -1x2
6 + 5x + 1x2 = -1x + x + x2 + -1x2

Combine like terms: -1x + x = 0
6 + 5x + 1x2 = 0 + x2 + -1x2
6 + 5x + 1x2 = x2 + -1x2

Combine like terms: x2 + -1x2 = 0
6 + 5x + 1x2 = 0

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

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 '(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 = {-3, -2}