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

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

Simplifying
3x2 + -6 = 4x + x2

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

Solving
-6 + 3x2 = 4x + x2

Solving for variable 'x'.

Reorder the terms:
-6 + -4x + 3x2 + -1x2 = 4x + x2 + -4x + -1x2

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

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

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

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

Factor out the Greatest Common Factor (GCF), '2'.
2(-3 + -2x + x2) = 0

Factor a trinomial.
2((-1 + -1x)(3 + -1x)) = 0

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

Simplifying
-1 + -1x = 0

Solving
-1 + -1x = 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 + -1x = 0 + 1

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

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

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

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

Simplifying
3 + -1x = 0

Solving
3 + -1x = 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 + -1x = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -1x = 0 + -3
-1x = 0 + -3

Combine like terms: 0 + -3 = -3
-1x = -3

Divide each side by '-1'.
x = 3

Simplifying
x = 3
Solution
x = {-1, 3}